What is the Least Common Multiple of 3189 and 3200?

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 3189 and 3200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3189 and 3200, than apply into the LCM equation.

GCF(3189,3200) = 1
LCM(3189,3200) = ( 3189 × 3200) / 1
LCM(3189,3200) = 10204800 / 1
LCM(3189,3200) = 10204800

Least Common Multiple (LCM) of 3189 and 3200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3189 and 3200. First we will calculate the prime factors of 3189 and 3200.

Prime Factorization of 3189

Prime Factorization of 3200

Now multiplying the highest exponent prime factors to calculate the LCM of 3189 and 3200.

LCM(3189,3200) = 3¹ × 1063¹ × 2⁷ × 5²
LCM(3189,3200) = 10204800