What is the Least Common Multiple of 37590 and 37600?

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 37590 and 37600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37590 and 37600, than apply into the LCM equation.

GCF(37590,37600) = 10
LCM(37590,37600) = ( 37590 × 37600) / 10
LCM(37590,37600) = 1413384000 / 10
LCM(37590,37600) = 141338400

Least Common Multiple (LCM) of 37590 and 37600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37590 and 37600. First we will calculate the prime factors of 37590 and 37600.

Prime Factorization of 37590

Prime Factorization of 37600

Now multiplying the highest exponent prime factors to calculate the LCM of 37590 and 37600.

LCM(37590,37600) = 2⁵ × 3¹ × 5² × 7¹ × 179¹ × 47¹
LCM(37590,37600) = 141338400