Problems on H.C.F and L.C.M - General Questions (2)
| 9. | 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: |
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Answer: Option C Explanation: Since the numbers are co-prime, they contain only 1 as the common factor. Also, the given two products have the middle number in common. So, middle number = H.C.F. of 551 and 1073 = 29;
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Required sum = (19 + 29 + 37) = 85.| 10. | The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is: |
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Answer: Option C Explanation: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm. |
| 11. | 252 can be expressed as a product of primes as: |
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Answer: Option A Explanation: Clearly, 252 = 2 x 2 x 3 x 3 x 7. |
| 12. | The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is: |
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Answer: Option B Explanation: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7 = 1015 |
| 13. | The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: |
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Answer: Option D Explanation: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48. |
| 14. | What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ? |
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Answer: Option B Explanation: L.C.M. of 12, 18, 21 30 2 | 12 - 18 - 21 - 30
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= 2 x 3 x 2 x 3 x 7 x 5 = 1260. 3 | 6 - 9 - 21 - 15
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Required number = (1260 � 2) | 2 - 3 - 7 - 5
= 630. |
| 15. | The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: |
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Answer: Option C Explanation: Other number = |
| 16. | 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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Answer: Option D Explanation: L.C.M. of 252, 308 and 198 = 2772. So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec. |