Question

LCM (p, q) × HCF (p, q) = pq

Answer 1

Heyy...

Step-by-step explanation:

P=a²b³

q=a³b

HCF (p,q) =a²b

LCM (p.q)=a³b³

As we know that HCF(p,q)xLCM(p,q)=a²bxa³b³

=a⁵b⁴ ---------- equation 1

pq=a²b³xa³b

=a⁵b⁴-----------equation 2

from 1 and 2

we can say that HCF(p,q)xLCM(p,q)=pq

Hope this helps

Answer 2

The multiple of LCM and HCF of two numbers is equal to the product of two numbers.

Given: $LCM (p, q)\times HCF (p, q) = pq$

For proofing the given relation, Let us consider two numbers be 6 and 8.

The Product of two numbers is

$6\times 8=48$

Factors of 6 and 8 is,

$6=2\times 3\\8=2^3$

$LCM(6,8)=2^3\times 3$

$LCM(6,8)=24$

$HCF(6,8)=2$

Hence, $LCM(6,8)\times HCF(6,8)=24\times 2$

$LCM(6,8)\times HCF(6,8)=48$