Written as a product of its prime factors, 1568=2^57^2 and 56=2^37. 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.

Question

Mathematics

Curtis Copeland

24 April, 05:34

Written as a product of its prime factors, 1568=2^57^2 and 56=2^37. 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.

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Answers (1)

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Kelvin Mendez · Answer 1

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.

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.

Written as a product of its prime factors, 1568=2^57^2 and 56=2^37. 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.