the product of two 2 digit numbers is 2028 and their g..., HCF & LCM, General Mathematics

Question:The product of two 2-digit numbers is 2028 and their G.C.M. is 13. The numbers are:

A 26,78 
B 39,52 
C 13,156 
D 36,68

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+ AnswerB

+ Explanationsolution:
Let the numbers be 13a and 13b.Then,
`13a xx 13b = 2028` 
`=> ab = 12`.
Now, co-primes with product 12 are `(1,12) and (3,4)`.
So, the numbers with H.C.F. 13 and product 2028 are:
`(13 xx 1, 13 xx 12) and (13 xx 3, 13 xx 4)`.
`:.` Required 2-digit numbers are `39 & 52`.

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