What is the Least Common Multiple of 31176 and 31185?

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 31176 and 31185 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31176 and 31185, than apply into the LCM equation.

GCF(31176,31185) = 9
LCM(31176,31185) = ( 31176 × 31185) / 9
LCM(31176,31185) = 972223560 / 9
LCM(31176,31185) = 108024840

Least Common Multiple (LCM) of 31176 and 31185 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31176 and 31185. First we will calculate the prime factors of 31176 and 31185.

Prime Factorization of 31176

Prime Factorization of 31185

Now multiplying the highest exponent prime factors to calculate the LCM of 31176 and 31185.

LCM(31176,31185) = 2³ × 3⁴ × 433¹ × 5¹ × 7¹ × 11¹
LCM(31176,31185) = 108024840