What is the Least Common Multiple of 45 and 165?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 45 and 165 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 165, than apply into the LCM equation.

GCF(45,165) = 15
LCM(45,165) = ( 45 × 165) / 15
LCM(45,165) = 7425 / 15
LCM(45,165) = 495

Least Common Multiple (LCM) of 45 and 165 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 165. First we will calculate the prime factors of 45 and 165.

Prime Factorization of 45

Prime Factorization of 165

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 165.

LCM(45,165) = 3² × 5¹ × 11¹
LCM(45,165) = 495