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Question

If the prime factorisation of a and b are a=22×3×x and b=2×32×y ; LCM of (a, b) =22×32×52 and HCF of (a, b) = 2×3×5, which of the following is true? (x1, y1)

A
xy = 25
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B
x + y = 30
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C
x – y = 0
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D
x = 6
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Solution

The correct option is B x + y = 30
Since product of two numbers = LCM × HCF
(22×3×x)×(2×32×y)=(2×3×5)×(22×32×52)
which gives xy=5×52
Therefore either x = 5 and y = 25 or x = 25 and y = 5.
We cannot specify respective values. But, we can say that the sum is always 25 + 5 = 30.

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