What is the Least Common Multiple of 1500 and 1512?

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 1500 and 1512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1500 and 1512, than apply into the LCM equation.

GCF(1500,1512) = 12
LCM(1500,1512) = ( 1500 × 1512) / 12
LCM(1500,1512) = 2268000 / 12
LCM(1500,1512) = 189000

Least Common Multiple (LCM) of 1500 and 1512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1500 and 1512. First we will calculate the prime factors of 1500 and 1512.

Prime Factorization of 1500

Prime Factorization of 1512

Now multiplying the highest exponent prime factors to calculate the LCM of 1500 and 1512.

LCM(1500,1512) = 2³ × 3³ × 5³ × 7¹
LCM(1500,1512) = 189000