Real Numbers Question - CBSE

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 $ ext{LCM}(p, q)$ is:
(a) $a b$
(b) $a^2 b^2$
(c) $a^3 b^2$
(d) $a^3 b^3$

Accepted Answer

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 $ ext{LCM}(p,q) = a^3 b^2$. [0.5 Mark]

---
🎯 Official CBSE Marking Scheme:
Correct identification of greatest powers: 0.5 Mark
Correct LCM expression: 0.5 Mark

Question:

Step-by-Step Solution

Master Real Numbers with Mathbee