Question

Two positive integers p and q are written as p= a^2b^3 and q = a^2b^3; a,b are prime numbers, then verify:
LCM(p,q) multiply by HCF(p,q) = pq

Answer 1

I think in question q= a³b 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= a³b

HCF(p,q)= a²b

LCM (p,q)= a³b³

HCF× LCM= a²b× a³b³= a^5b⁴

HCF× LCM=a^5b⁴...........(1)

p ×q= a²b³× a³b= a^5b⁴

p ×q= = a^5b⁴..................(2)

Lcm (p,q) × Hcf(p,q) = pq

a^5b⁴ = a^5b⁴
[From equation 1 and 2]

Verified,..

Hope this will help you....