What is the Least Common Multiple of 37000 and 37014?

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 37000 and 37014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37000 and 37014, than apply into the LCM equation.

GCF(37000,37014) = 2
LCM(37000,37014) = ( 37000 × 37014) / 2
LCM(37000,37014) = 1369518000 / 2
LCM(37000,37014) = 684759000

Least Common Multiple (LCM) of 37000 and 37014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37000 and 37014. First we will calculate the prime factors of 37000 and 37014.

Prime Factorization of 37000

Prime Factorization of 37014

Now multiplying the highest exponent prime factors to calculate the LCM of 37000 and 37014.

LCM(37000,37014) = 2³ × 5³ × 37¹ × 3¹ × 31¹ × 199¹
LCM(37000,37014) = 684759000