# What is the least common multiple of p and q if p, q are prime numbers ?

May 22, 2015

If $p$ and $q$ are distinct primes then the LCM (least common multiple) of $p$ and $q$ is $\left(p \times q\right)$. This is the smallest number divisible by both $p$ and $q$.

If $p = q$ then the LCM of $p$ and $q$ is $p$.

May 22, 2015

A prime number is a natural number greater than 1 which has no divisor other than 1 and itself.

example : $2 , 3 , 5 , 7 , 11 , 13. . .$ etc

The least common multiple (LCM) of two numbers is the smallest non zero number which is a multiple of both numbers.

considering the L.C.M of two primes :

• $2 \mathmr{and} 3$ , here the L.C.M = $2 \times 3 = 6$
• $3 \mathmr{and} 5$ , L.C.M = $3 \times 5 = 15$
• $2 \mathmr{and} 7$ , L.C.M = $2 \times 7 = 14$

so if $p$ and $q$ are primes L.C.M $= p \times q = p q$