If two positive integers p and q are written as p=a^2b^3 and q=a^3b; a,b are prime numbers,then verify:LCM(p,q)*HCF(p,q]=pc
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p=a2b3=a×a×b×b×b
q=a3b =a×a×a×b
hcf=a×a×b=a2b
lcm=a2b×ab2=a3b3
hcf×lcm=pq
a2b ×a3b3 =a2b3 ×a3b
a5b4 =a5b4
hence proved
q=a3b =a×a×a×b
hcf=a×a×b=a2b
lcm=a2b×ab2=a3b3
hcf×lcm=pq
a2b ×a3b3 =a2b3 ×a3b
a5b4 =a5b4
hence proved
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