What is the Least Common Multiple of 43500 and 43512?

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 43500 and 43512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43500 and 43512, than apply into the LCM equation.

GCF(43500,43512) = 12
LCM(43500,43512) = ( 43500 × 43512) / 12
LCM(43500,43512) = 1892772000 / 12
LCM(43500,43512) = 157731000

Least Common Multiple (LCM) of 43500 and 43512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43500 and 43512. First we will calculate the prime factors of 43500 and 43512.

Prime Factorization of 43500

Prime Factorization of 43512

Now multiplying the highest exponent prime factors to calculate the LCM of 43500 and 43512.

LCM(43500,43512) = 2³ × 3¹ × 5³ × 29¹ × 7² × 37¹
LCM(43500,43512) = 157731000