If two positive integers p and q are written as p = a2b3and q = a3b; a, b are primenumbers, then verify: LCM (p, q) × HCF (p, q) = pq
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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
so
lcm×hcf=pq
a3b3 ×a2b=a2b3 ×a3b
a5b4 =a5b4
hence proved
q=a3b=a×a×a×b
hcf=a×a×b=a2b
lcm= a2b×ab2 =a3b3
so
lcm×hcf=pq
a3b3 ×a2b=a2b3 ×a3b
a5b4 =a5b4
hence proved
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2
Answer:
pq
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