What is the Least Common Multiple of 31200 and 31213?

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 31200 and 31213 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31200 and 31213, than apply into the LCM equation.

GCF(31200,31213) = 13
LCM(31200,31213) = ( 31200 × 31213) / 13
LCM(31200,31213) = 973845600 / 13
LCM(31200,31213) = 74911200

Least Common Multiple (LCM) of 31200 and 31213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31200 and 31213. First we will calculate the prime factors of 31200 and 31213.

Prime Factorization of 31200

Prime Factorization of 31213

Now multiplying the highest exponent prime factors to calculate the LCM of 31200 and 31213.

LCM(31200,31213) = 2⁵ × 3¹ × 5² × 13¹ × 7⁴
LCM(31200,31213) = 74911200