The sum of two numbers is 52 and their L.C.M is168.Find the two numbers.

Asked by vakul.goyle | 30th Apr, 2010, 10:16: AM

Expert Answer:

we know that the addition of two numbers is divisile by their HCF

So if H is the HCF of the given numbers then H divides the sum 52.

so H is a factor of 52

also H must be a factor of the LCM.(as the hcf of two numbers has to be a factor of their lcm)

so H must be the hcf of 52 and 168

so H=4

product of two numbers= product of hcf and lcm

let one number be x, so the other number must be 52-x

so

x(52-x)=4 x 168

(x-24)(x-28)=0

x=24 or 28

Answered by  | 4th May, 2010, 08:28: PM

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