What is the Least Common Multiple of 37200 and 37206?

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 37206 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 37206, than apply into the LCM equation.

GCF(37200,37206) = 6
LCM(37200,37206) = ( 37200 × 37206) / 6
LCM(37200,37206) = 1384063200 / 6
LCM(37200,37206) = 230677200

Least Common Multiple (LCM) of 37200 and 37206 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37200 and 37206. First we will calculate the prime factors of 37200 and 37206.

Prime Factorization of 37200

Prime Factorization of 37206

Now multiplying the highest exponent prime factors to calculate the LCM of 37200 and 37206.

LCM(37200,37206) = 2⁴ × 3³ × 5² × 31¹ × 13¹ × 53¹
LCM(37200,37206) = 230677200