The LCM of two prime numbers p

Question

The LCM of two prime numbers $p a n d q (p > q)$ is 221. Find the value of 3p−q.

Smart Achievers · Accepted Answer

(3)

p and q (p > q) are prime numbers, HCF (p,q) = 1

Given, LCM (p,q) = 221

$\Rightarrow L C M (p, q) \times H C F (p, q) = p \times q \Rightarrow 1 \times 221 = p \times q \Rightarrow p \times q = 221 S o, p = 17, q = 13 (∵ p > q) 3 p - q = 3 \times 17 - 13 = 51 - 13 = 38$

Solution

Q.
The LCM of two prime numbers $p a n d q (p > q)$ is 221. Find the value of 3p−q.

1 4

2 28

3 38

4 48

Ans.
(3)

p and q (p > q) are prime numbers, HCF (p,q) = 1

Given, LCM (p,q) = 221

$\Rightarrow L C M (p, q) \times H C F (p, q) = p \times q \Rightarrow 1 \times 221 = p \times q \Rightarrow p \times q = 221 S o, p = 17, q = 13 (∵ p > q) 3 p - q = 3 \times 17 - 13 = 51 - 13 = 38$

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