What is the Least Common Multiple of 37200 and 37210?

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 37200 and 37210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37200 and 37210, than apply into the LCM equation.

GCF(37200,37210) = 10
LCM(37200,37210) = ( 37200 × 37210) / 10
LCM(37200,37210) = 1384212000 / 10
LCM(37200,37210) = 138421200

Least Common Multiple (LCM) of 37200 and 37210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37200 and 37210. First we will calculate the prime factors of 37200 and 37210.

Prime Factorization of 37200

Prime Factorization of 37210

Now multiplying the highest exponent prime factors to calculate the LCM of 37200 and 37210.

LCM(37200,37210) = 2⁴ × 3¹ × 5² × 31¹ × 61²
LCM(37200,37210) = 138421200