Question

The ratio of the three numbers is 2: 3: 6 and their lcm is72 then how is their hcm

Answer 1

Let x be the unknown common factor among the numbers,

Then the no/s become as 2x, 3x, 6x.

Now all factors among these are 2, 3, x

Then LCM = Product of all factors

             72 = 2×3×(x)

             72 = 6x

                x = 12
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Then the no/s are are 24, 36, 72

We know that, 

HCF(24,36,72) =          (24×36×72) × LCM(24,36,72) 
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                             LCM(24,36) × LCM(36,72) × LCM(72,24)

                         = 12
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Hence HCF = 12
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