# If two positive i

First, we’ll find HCF (p, q), when p = a2b and q = a3b.

p = a2b3

= a × a × b × b × b

q = a3b

= a × a × a × b

Common factors are a, a and b.

Thus, HCF (p, q) = a × a × b = a2b …(i)

Now, let’s find LCM (p, q).

We have

LCM (p, q) = a × a × a × b × b × b = a3b3 …(ii)

To verify LCM (p, q) × HCF (p, q) = pq,

Taking LHS:

LCM (p, q) × HCF (p, q) = a2b × a3b3 [ from equations (i) & (ii)]

= a2+3b1+3

= a5b4 …(iii)

Taking RHS:

pq = a2b3 × a3b

= a2+3b3+1

= a5b4 …(iv)

LHS = RHS

This means that it is verified LCM (p, q) × HCF (p, q) = pq.

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