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Question
If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is ______.
Options
ab
a2b2
a3b2
a3b3
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Solution
If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is `underline(bb(a^3b^2))`.
Explanation:
Given that, p = ab2 = a × b × b
And q = a3b = a × a × a × b
LCM of p and q = LCM (ab2, a3b)
= a × b × b × a × a
= a3b2 .........[Since, LCM is the product of the greatest power of each prime factor involved in the numbers]
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