Question

3. If a = pq2

, b = p3q, p and q are prime numbers then ___ is the LCM (a, b)​

Answer 1

AnswEr:-

Given:-

• a = pq².
• b = p³q.

To Find:-

• LCM (a,b).

So Here,

=》 a = pq².

Which can be written as,

=》 a = p × q².

=》 a = p × q × q.

Similarly,

=》 b = p³q.

Which can be written as,

=》 b = p³ × q.

=》 b = p × p × p × q.

Therefore LCM (a,b):-

= p × p × p × q × q.

= p³ × q².

= p³q².

So if a = pq², b = p³q, p and q are prime numbers then p³q² is the LCM (a, b).

Similarly We can also Find out HCF (p,q):-

• a = p × q × q.

• b = p × p × p × q.

Therefore HCF (p,q),

= p × q

= pq.

So HCF (p,q) = pq.

Answer 2

★ Given :

• a = pq²
• b = p³q
• a and b bith are prume numbers

★ To Find :

We have to find the LCM of a and b.

★ Explanation :

As, we have to calculate the LCM of a and b. So, firstly we will make the factors of a and b.

A.T.Q

$\sf{\dashrightarrow a = pq^2} \\ \\ \sf{\dashrightarrow a = p \times q \times q.....(1)}$

So, Factors of a = p * q * q

Now,

$\sf{\dashrightarrow b = p^3q} \\ \\ \sf{\dashrightarrow b = p \times p \times p \times q.....(2)}$

So, Factors of b = p * p * p * q

Now, we will calculate LCM by using equation (1) and (2) resectively.

$\sf{\dashrightarrow LCM = p \times p \times p \times q \times q} \\ \\ \sf{\dashrightarrow LCM = p^3 \times q^2} \\ \\ \sf{\dashrightarrow LCM = p^3q^2} \\ \\ \large{\star{\underline{\boxed{\sf{LCM = p^3 q^2}}}}}$

So, If a = pq², b = p³q, p and q are prime numbers then p³q² is the LCM (a,b).

$\rule{400}{4}$