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

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 2)
2.
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
276
299
322
345
Explanation:

Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322.

Discussion:
144 comments Page 1 of 15.

Aditya uniyal said:   5 months ago
Please correct me, if I am wrong:

Let two numbers be A and B. It is given that their HCF is 23.

Therefore, A = 23 * x
and B = 23 * y, where x and y are coprime pairs, so according to the property of coprime LCM(x,y) = xy.

And we can find their LCM as follows: LCM(A, B) =LCM(23*x, 23*y) = 23 * x * y.

Therefore, x and y are the other two factors of LCM, and we are given that those 2 factors are 13 and 14 respectively.

Therefore x = 13 and y = 14.

And hence largest number = 23 * 14 = 322.
(5)

Pratyusha 2 said:   6 months ago
Very helpful, thanks for explaining @Lahari.
(1)

Good explanation @Lahari.

Sachin alure said:   10 months ago
Well explained @Krishna.

Nitish said:   11 months ago
Thank you for explaining the answer @Krishna.

Saeed said:   1 year ago
Thanks alot. @Dheeraj.

Krishna said:   2 years ago
Please correct me if I am wrong:

Let two numbers be A and B. It is given that their HCF is 23. Therefore, A = 23 * x
and B = 23 * y, where x and y are any integers.

And we can find their LCM as follows: LCM(A, B) = 23 * x * y.

Therefore, x and y are the other two factors of LCM, and we are given that those 2 factors are 13 and 14 respectively.

Therefore x = 13 and y = 14. And hence largest number = 23 * 14 = 322.

Karan said:   2 years ago
@Ahmed.

Yeah, right, good explanation. Thanks.

Ysr said:   2 years ago
@Chiya.

Good explained. Thanks.

Khushi said:   2 years ago
Number 1 = a * 23
number 2 = b * 23
And other factors of LCM are 13 and 14
So clearly a * b = 13 * 14

But my point is:
a * b = 26 * 7
a * b = 81 * 2
As they are co prime in themselves,