Real Numbers · Class 10 · CBSE Mathematics

If two positive integers p and q can be expressed as p = ab^2 and q = a^3b, where a, b are prime numbers, then what is the LCM(p, q)?

Practice question from Real Numbers (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-D3340C

If two positive integers $p$ and $q$ can be expressed as $p = ab^2$ and $q = a^3b$ , where $a, b$ are prime numbers, then what is the LCM( $p, q$ )?

A. $ab$
B. $a^2b^2$
C. $a^3b^2$ Correct answer
D. $a^3b^3$

Solution

The LCM of two numbers given in prime factorized form is the product of the greatest power of each prime factor involved. For $p = a^1b^2$ and $q = a^3b^1$ , the greatest power of $a$ is $a^3$ and of $b$ is $b^2$ . Thus, $\text{LCM}(p, q) = a^3b^2$ .

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