What is the Least Common Multiple of 43185 and 43200?

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 43185 and 43200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43185 and 43200, than apply into the LCM equation.

GCF(43185,43200) = 15
LCM(43185,43200) = ( 43185 × 43200) / 15
LCM(43185,43200) = 1865592000 / 15
LCM(43185,43200) = 124372800

Least Common Multiple (LCM) of 43185 and 43200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43185 and 43200. First we will calculate the prime factors of 43185 and 43200.

Prime Factorization of 43185

Prime Factorization of 43200

Now multiplying the highest exponent prime factors to calculate the LCM of 43185 and 43200.

LCM(43185,43200) = 3³ × 5² × 2879¹ × 2⁶
LCM(43185,43200) = 124372800