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- Problems on H.C.F and L.C.M
41.
Which of the following has most number of divisors?
- A.99
- C.176
- B.101
- D.182
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| 99 = 1 x 3 x 3 x 11; 101 = 1 x 101; |
| 176 = 1 x 2 x 2 x 2 x 2 x 11; 182 = 1 x 2 x 7 x 13 |
| So, divisors of 99 are 1, 3, 9, 11, 33 and 99; |
| divisors of 101 are 1 and 101; |
| divisiors of 176 are 1, 2, 4, 8, 16, 22, 44, 88 and 176; |
| divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182. |
| Hence, 176 has the most number of divisors. |
42.
The H.C.F. of 0.54, 1.8 and 7.2 is:
- A.1.8
- C.0.018
- B.0.18
- D.18
- Answer & Explanation
- Report
Answer : [B]
Explanation :
Explanation :
| Given numbers are 0.54, 1.80 and 7.20. H.C.F. of 54, 180 and 720 is 18. | |||
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43.
The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is:
- A.1600
- C.6400
- B.3600
- D.14400
- Answer & Explanation
- Report
Answer : [B]
Explanation :
Explanation :
| The least number divisible by 16, 20, 24 = L.C.M. of 16, 20, 24 = 240 = 2 x 2 x 2 x 2 x 3 x 5 | |||
| To make it a perfect square, it must be multiplied by 3 x 5 | |||
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44.
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
- A.12
- C.24
- B.16
- D.48
- Answer & Explanation
- Report
Answer : [D]
Explanation :
Explanation :
| Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. |
| So, the numbers are 12 and 16. |
| L.C.M. of 12 and 16 = 48 |
45.
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
- A.9000
- C.9600
- B.9400
- D.9800
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| Greatest number of 4 digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600 | |||
| On dividing 9999 by 600, the remainder is 399 | |||
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