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.

Hello,

Let's assume

a the lowest number

b the tallest.

HCF (a, b) = 56

LCM (a, b) = 1568

a*b=HCF*LCM = (2^5*7^2) * (2^3*7) = 2^8*7^3

a=56*x

b=56*y

a*b=56²*x*y==>x*y=2^2*7

The numbers possible are (56*1,56*28), (56*2,56*14), (56*4,56*7)

(56*1,56*28) = (56,1568) is excluded.

(56*2,56*14) = (112,784) has like HCF=112 and not 56.

The answer is (56*4,56*7) = (224,392) which HCF is 56 and LCM=1568.