Question

The L.C.M. of two numbers is 196 and their H.C.F. is 7. If the difference of the two numbers is 21, find the larger of the two numbers​

Answer 1

Answer:

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Step-by-step explanation:

Let the larger number be x,

So, smaller number= 21 - x

LCM X HCF = Product of the two numbers

(196)*(7) = (x)(21-x)

1372 = 21x + x^2

x^2 + 21x -1372 = 0

x^2 + 28x - 49x - 1372 = 0

x(x + 28) - 49(x + 28) = 0

(x + 28)(x - 49) = 0

x = 49, -28

x ≠ -28 ( because when we put this in 21-x then the smaller number becomes greater than larger number)

so, x = 49

Therefore, the larger number is 49