Question

If two positive integers p and q are written as p=a2b3 and q=a2b and a and b are prime no and verify when lcmpq×hcf of p.q. =p.q

Answer 1

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Answer 2

HCF of two or more numbers is the product of the smallest power of each common prime factors involved in the numbers.

LCM of two or more numbers is a product of the greatest power of its prime factors involved in the numbers with highest power.


SOLUTION:

Given:

p = a²b³

q= a²b

HCF(p,q)= a²b

LCM (p,q)= a²b³

HCF× LCM= a²b× a²b³= a⁴b⁴

HCF× LCM=a⁴b⁴...........(1)

p ×q= a²b³× a²b= a⁴b⁴

p ×q= = a⁴b⁴..................(2)

Lcm (p,q) × Hcf(p,q) = pq

a⁴b⁴ = a⁴b⁴
[From equation 1 and 2]

Verified,..

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