If two positive integers p and q are written as p = a^2b^3 and q = a^3b, where a and b are integers, then show that LCM (p, q) * HCF (p, q) = pq

Question

Mathematics

Hubbard

14 January, 17:47

If two positive integers p and q are written as p = a^2b^3 and q = a^3b, where a and b are integers, then show that LCM (p, q) * HCF (p, q) = pq

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Answers (1)

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Louis Sawyer · Answer 1

The LCM is the lowest expression that both p and q divide into.

LCM (p, q) = a^3b^3

The HCF is the highest common factor of p and q:-

HCF (p, q) = a^2b

HCF (p, q) * LCM (p, q) = a^3b^3 * a^2b = a^5b^4 and

pq = a^2b^3 * a^3b = a^5b^4

Therefore HCF (p, q) * LCM (p, q) = pq