Q. 74.0( 10 Votes )

If two positive i

Answer :

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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