What is the Least Common Multiple of 31185 and 31200?

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 31185 and 31200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31185 and 31200, than apply into the LCM equation.

GCF(31185,31200) = 15
LCM(31185,31200) = ( 31185 × 31200) / 15
LCM(31185,31200) = 972972000 / 15
LCM(31185,31200) = 64864800

Least Common Multiple (LCM) of 31185 and 31200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31185 and 31200. First we will calculate the prime factors of 31185 and 31200.

Prime Factorization of 31185

Prime Factorization of 31200

Now multiplying the highest exponent prime factors to calculate the LCM of 31185 and 31200.

LCM(31185,31200) = 3⁴ × 5² × 7¹ × 11¹ × 2⁵ × 13¹
LCM(31185,31200) = 64864800