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Real Numbers
RD Sharma
CBSE
Grade 10
Question:
If two positive integers $p$ and $q$ can be expressed as $p = a b^2$ and $q = a^3 b$, where $a, b$ are prime numbers, then $\text{LCM}(p, q)$ is: (a) $a b$ (b) $a^2 b^2$ (c) $a^3 b^2$ (d) $a^3 b^3$
Step-by-Step Solution
Key Concept: $\text{LCM}$ is the product of greatest powers of each prime factor involved.
Greatest exponent of $a$ is $3$, greatest exponent of $b$ is $2$. [0.5 Mark] $\text{LCM}(p,q) = a^3 b^2$. [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Identifying highest powers of prime factors: 0.5 Mark Writing $\text{LCM} = a^3 b^2$: 0.5 Mark
Correct Answer:$a^3 b^2$
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