LCM and HCF Questions
1. Find the least number which when divided by 12, 27 and 35 leaves 6 as a remainder?
3586 3756 3786 4786 None of these
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2. Find the 4-digit smallest number which when divided by 12, 15, 25, 30 leaves no remainder?
1300 1400 1200 1500 None of these
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3. Find the least number which when divided by 2, 3, 4 and 5 leaves a remainder 3. But when divided by 9 leaves no remainder?
33 63 183 153 None of these
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4. Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
27 36 43 400 None of these
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5. Find the greatest number which when divides 564 and 467 leaves the remainder as 4 and 7 respectively.
30 20 25 35 None of these
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6. The product of LCM and HCF of two numbers is 48. The difference of two numbers is 8. Find the numbers?
1, 48 6, 8 3, 16 4, 12 None of these
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7. Four different electronic devices make a beep after every 30 minutes, 1 hour, 1 hour 30 minutes and 1 hour 45 minutes respectively. All the device beeped together at 12 noon. They will again beep together at
3:00 AM 12 Midnight 6:00 AM 9:00 AM None of these
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8. What is the LCM of (6x³ + 60x² + 150x) and (3xâ´ + 12x³ – 15x²)?
6x2(x + 5)2(x – 1) 3x2(x + 5)2(x – 1) 6x2(x + 5)2(x – 1)2 3x2(x + 5)(x – 1)2 None of these
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9. On dividing a number by 4, the remainder is 2. The quotient so obtained when divided by 5, leaves the remainder 3. Now the quotient so obtained when divided by 6, leaves the remainder 5. The last quotient is 7. The number was
962 954 946 938 None of these
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10. The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is24, then the other number is
48 36 24 16 None of these
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11. HCF of 2/3, 4/5 and 6/7 is
48/105 2/105 16/105 24/105 None of these
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12. What is the LCM of 120 and 450?
2400 1800 3600 4800 None of these
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13. HCF of x2 - y2 and x3 - y3 is
x - y x3 - y3 x2 - y2 None of these Cannot be determined
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14. The HCF of two numbers is 24. The number which can be their LCM is
84 120 128 148 None of these
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15. The sum of two number is 528 and their HCF is 33. How many pairs of such numbers can be?
1 2 3 4 None of these
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16. Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is
100 80 60 50 None of these
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17. The length, breadth and height of a room are 363m, 528m and 693m respectively. Determine the longest tape that can measure the three dimensions of the room exactly.
33 metre 35 metre 27 metre 30 metre None of these
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18. The product of two numbers is 35828 and their HCF is 26. Find their LCM.
931788 689 1378 3583 None of these
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19. Find the highest common factor of 72 and 168.
12 24 6 63 None of these
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20. The HCF of 252, 294 and 3#8 is 42, what is #?
2 4 8 7 None of these
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21. What is the least number which when divided by 7, 9 and 12 leaves the same remainder 1 in each case?
253 352 505 523 None of these
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22. The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?
24 48 56 60 None of these
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23. The LCM of two numbers is 30 and their HCF is 5. One of the numbers is 10. The other is
20 25 15 5 None of these
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24. What is the HCF of 150, 225 and 375?
15 25 75 125 None of these
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25. Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is
21 24 28 84 None of these
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26. If the product of two numbers is 2160 and the HCF is 6, then the ratio of HCF and LCM is
1 : 60 60 : 1 21 : 60 60 : 21 None of these
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27. Find the complete remainder when a certain number divided successively by 3, 5 and 7 leaves remainders 2, 3 and 4 respectively?
61 52 73 71 None of these
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28. The product of two 2-digit numbers is 2160 and their H.C.F. is 12. The numbers are
(12, 60) (72, 30) (36, 60) (60, 70) None of these
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29. Find the HCF of (4 * 54 * 3125), (16 *5 * 8) and (32 * 27 * 11 * 49).
8 24 4 40 None of these
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30. The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is
40 42 50 52 32
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31. Find the LCM of 25, 30 and 60.
600 240 150 300 None of these
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32. The HCF of two numbers is 8. Which one of the following can never be their LCM?
24 48 56 60 None of these
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33. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
28 32 40 64 None of these
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34. Which of the following has the most number of divisors ?
99 101 176 182 None of these
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35. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
123 127 235 305 None of these
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36. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
504 536 544 548 None of these
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37. Find the highest common factor of 36 and 84.
4 6 12 18 None of these
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38. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
75 81 85 89 None of these
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39. The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
1008 1015 1022 1032 None of these
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40. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
12 16 25 48 None of these
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41.What will be the least number which when doubled What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
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42. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
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43. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
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44. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
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45. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:-
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46. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
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47. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
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48. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
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49. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
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50. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
will be exactly divisible by 12, 18, 21 and 30 ?
196 630 1260 2520 None of these
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42. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
26 minutes and 18 seconds 42 minutes and 36 seconds 45 minutes 46 minutes and 12 seconds None of these
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43. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
1677 1683 1987 2523 None of these
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44. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
3 13 23 33 None of these
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45. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:-
1 2 3 4 None of these
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46. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
101 107 111 185 None of these
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47. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
9000 9400 9600 9800 None of these
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48. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
4 5 6 8 None of these
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49. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
4 10 15 16 None of these
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50. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
4 7 9 13 None of these
