Aptitude - Problems on H.C.F and L.C.M

Exercise : Problems on H.C.F and L.C.M - General Questions
16.
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:
279
283
308
318
Answer: Option
Explanation:
Other number = 11 x 7700 = 308.
275

17.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
196
630
1260
2520
Answer: Option
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 รท 2) | 2 - 3 - 7 - 5

= 630.

18.
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
12
16
24
48
Answer: Option
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.


19.
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
1008
1015
1022
1032
Answer: Option
Explanation:

Required number = (L.C.M. of 12,16, 18, 21, 28) + 7

   = 1008 + 7

   = 1015


20.
252 can be expressed as a product of primes as:
2 x 2 x 3 x 3 x 7
2 x 2 x 2 x 3 x 7
3 x 3 x 3 x 3 x 7
2 x 3 x 3 x 3 x 7
Answer: Option
Explanation:
Clearly, 252 = 2 x 2 x 3 x 3 x 7.