Question 85

If the l.c.m. of the positive integers a and b is 60 and $$a^2 . b^2 = 32400$$, then the g.c.d. of a and b is

Solution

Concept Used: Product of two numbers = (L.C.M of numbers) x (G.C.D of numbers)

Here

$$a^2 . b^2 = 32400$$

Hence a.b = $$\sqrt{\ 32400}$$ = 180 =Product of Numbers

Given L.C.M. = 60

So axb = (l.c.m) x( g.c.d)

180 = 60 x g.c.d

g.c.d = 3 Answer

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