Question

8. If two positive integers p and q are written as p = a2b3 and q = a3b; a, b are prime numbers, then verify: lcm (p, q) hcf (p, q) = pq.

Answer 1

Answer:

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The prime factorization of p is p = a²b³

The prime factorization of q is q = a³b

To get the lcm, we take the larger exponent for each prime.

So lcm(p, q) = a³b³.

To get the hcf, we take the smaller exponent for each prime.

So gcd(p, q) = a²b

Then

lcm(p, q) gcd(p,q)

= a³b³ × a²b

= a²b³ × a³b   ( we can change the order of multiplication )

= pq