What is the Least Common Multiple of 43488 and 43500?

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 43488 and 43500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43488 and 43500, than apply into the LCM equation.

GCF(43488,43500) = 12
LCM(43488,43500) = ( 43488 × 43500) / 12
LCM(43488,43500) = 1891728000 / 12
LCM(43488,43500) = 157644000

Least Common Multiple (LCM) of 43488 and 43500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43488 and 43500. First we will calculate the prime factors of 43488 and 43500.

Prime Factorization of 43488

Prime Factorization of 43500

Now multiplying the highest exponent prime factors to calculate the LCM of 43488 and 43500.

LCM(43488,43500) = 2⁵ × 3² × 151¹ × 5³ × 29¹
LCM(43488,43500) = 157644000