ZhiHeng
Answered

Written as a product of its prime factors, 1568=2^5×7^2 and 56=2^3×7. If the LCM and HCF of two numbers are 1568 and 56 respectively, find these two numbers, given that the numbers are not 56 and 1568.

Verified Answer :

caylus

Hello,

Let's assume
a the lowest number
b the tallest.

HCF(a,b)=56
LCM(a,b)=1568

ab=HCFLCM=(2^57^2)(2^37)=2^87^3

a=56x
b=56y

ab=56²xy==>xy=2^27

The numbers possible are (561,5628),(562,5614),(564,567)
(561,5628)=(56,1568) is excluded.
(562,5614)=(112,784) has like HCF=112 and not 56.

The answer is (564,56*7)=(224,392) which HCF is 56 and LCM=1568.

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