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- Problems on H.C.F and L.C.M
16.
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8, is:
- A.504
- C.544
- B.536
- D.548
- Answer & Explanation
- Report
Answer : [D]
Explanation :
Explanation :
| Required number = (L.C.M. of 12, 15, 20, 54) + 8 | |||
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17.
The H.C.F. and L.C.M. of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:
- A.12
- C.84
- B.48
- D.108
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| Let the numbers be x and 4x, | |||||||||||||||||
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| Hence, larger number = 4x = 84 | |||||||||||||||||
18.
Find the least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
- A.17004
- C.18002
- B.18000
- D.18004
- Answer & Explanation
- Report
Answer : [D]
Explanation :
Explanation :
| L.C.M. of 16, 18, 20, 25 = 3600. | |||
| Required number is of the form 3600k + 4 | |||
| Least value of k for which (3600k + 4) is divisible by 7 is k = 5. | |||
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19.
Which of the following fractions is the largest?
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A.
7 8 -
C.
31 40
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B.
13 16 -
D.
63 80
- Answer & Explanation
- Report
Answer : [A]
Explanation :
Explanation :
| L.C.M. of 8, 16, 40 and 80 = 80 | ||||||||||||||||||||||||||||||
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20.
Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively.
- A.3002
- C.3024
- B.3013
- D.3036
- Answer & Explanation
- Report
Answer : [B]
Explanation :
Explanation :
| Here (18 - 7) = 11, (21 - 10) = 11 and (24 - 13) = 11. | |||
| L.C.M. of 18, 21 and 24 is 504. | |||
| Let required number be 504k – 11. | |||
| Least value of k for which (504k - 11) is divisible by 23 is k = 6 | |||
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