What is the Least Common Multiple of 37600 and 37614?

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 37600 and 37614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37600 and 37614, than apply into the LCM equation.

GCF(37600,37614) = 2
LCM(37600,37614) = ( 37600 × 37614) / 2
LCM(37600,37614) = 1414286400 / 2
LCM(37600,37614) = 707143200

Least Common Multiple (LCM) of 37600 and 37614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37600 and 37614. First we will calculate the prime factors of 37600 and 37614.

Prime Factorization of 37600

Prime Factorization of 37614

Now multiplying the highest exponent prime factors to calculate the LCM of 37600 and 37614.

LCM(37600,37614) = 2⁵ × 5² × 47¹ × 3¹ × 6269¹
LCM(37600,37614) = 707143200