What is the Least Common Multiple of 39192 and 39200?

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 39192 and 39200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39192 and 39200, than apply into the LCM equation.

GCF(39192,39200) = 8
LCM(39192,39200) = ( 39192 × 39200) / 8
LCM(39192,39200) = 1536326400 / 8
LCM(39192,39200) = 192040800

Least Common Multiple (LCM) of 39192 and 39200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39192 and 39200. First we will calculate the prime factors of 39192 and 39200.

Prime Factorization of 39192

Prime Factorization of 39200

Now multiplying the highest exponent prime factors to calculate the LCM of 39192 and 39200.

LCM(39192,39200) = 2⁵ × 3¹ × 23¹ × 71¹ × 5² × 7²
LCM(39192,39200) = 192040800