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Two positive integers a and $b$ can be written as $a = p^{3} q^{2}$ and $b = p q^{3}$ , where $p$ and $q$ are distinct primes.
What is LCM(a, b)?

Class 10HCF and LCMNumber Systems

A $p^{3} q^{3}$
B $p q^{2}$
C $p^{4} q^{5}$
D $p^{3} q^{2}$

Step-by-Step Solution

LCM takes the highest power of each prime:

p^{m}

ax(3,1) =

p^{3}, q^{m}

ax(2,3) =

q^{3}

. So LCM =

p^{3} q^{3}

.

Answer: A)

p^{3} q^{3}

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