# 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:

Answer: Option

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.

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)

JaGaDeeSh said:
8 months ago

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.

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.

Yeah, right, good explanation. Thanks.

Ysr said:
2 years ago

@Chiya.

Good explained. Thanks.

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,

So why is the answer not 23*81? Please explain.

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,

So why is the answer not 23*81? Please explain.

(1)

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