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If two positive integers a and b are written as a=x $y^{2}$ and b = $x^{3}$ y, where x, y are prime numbers, then find LCM (a, b).

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LCM (a, b) = x^{3} y^{2}

LCM (b, b) = x^{2} y^{2}

LCM (a, a) = x^{} y^{2}

LCM (b, a) = x^{2} y^{3}

answer is A.

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Detailed Solution

Given that two positive integers are a=x

y^{2}

and b =

x^{3}

y, where x, y are prime numbers.
A number p is divisible by q if remainder of

\frac{p}{q}

is zero.
HCF of two or more integer is the largest positive integer which divides all the given integers.
LCM of two or more integer is the smallest common multiple of all integers such that it is divisible by all the given integers.
Factorizing a,

a = x \times y \times y

Factorizing b,

b = x \times x \times x \times y

LCM of a,b is given as

LCM (a, b) = x \times x \times x \times y \times y

LCM (a, b) = x^{3} y^{2}

Hence, option 1 is correct answer.

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