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If $p = a^{2} x b^{3}$ and $q = a^{3} x b$ , where a and $b$ are distinct primes, then LCM $(p$ , q) is:

Class 10Fundamental Theorem of ArithmeticNumber Systems

A $a^{3} x b^{3}$
B $a^{2} x b$
C $a^{5} x b^{4}$
D $a^{2} x b^{3}$

Step-by-Step Solution

LCM takes the highest power of each prime:

a^{3}

(from q) and

b^{3}

(from p), giving

a^{3} x b^{3}

.

Answer: A)

a^{3} x b^{3}

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