Real Numbers
NCERT Exemplar Ch 01
CBSE_NCERT_EXEMPLAR_CH01
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:
$a b$
$a^2 b^2$
$a^3 b^2$
$a^3 b^3$
Step-by-Step Solution
Key Concept: The LCM of numbers expressed in prime factors is the product of the greatest power of each prime factor involved.
Stepwise Solution:
Given $p = a^1 b^2$ and $q = a^3 b^1$. [0.5 Mark]
The greatest power of prime factor $a$ is $a^3$, and of prime factor $b$ is $b^2$. Thus $\text{LCM}(p,q) = a^3 b^2$. [0.5 Mark]
Marking Scheme:
• Correct identification of greatest powers: 0.5 Mark
• Correct LCM expression: 0.5 Mark
Correct Answer: $a^3 b^2$
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