What is the Least Common Multiple of 1650 and 1665?

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 1650 and 1665 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1650 and 1665, than apply into the LCM equation.

GCF(1650,1665) = 15
LCM(1650,1665) = ( 1650 × 1665) / 15
LCM(1650,1665) = 2747250 / 15
LCM(1650,1665) = 183150

Least Common Multiple (LCM) of 1650 and 1665 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1650 and 1665. First we will calculate the prime factors of 1650 and 1665.

Prime Factorization of 1650

Prime Factorization of 1665

Now multiplying the highest exponent prime factors to calculate the LCM of 1650 and 1665.

LCM(1650,1665) = 2¹ × 3² × 5² × 11¹ × 37¹
LCM(1650,1665) = 183150