What is the Least Common Multiple of 31080 and 31098?

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 31080 and 31098 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31080 and 31098, than apply into the LCM equation.

GCF(31080,31098) = 6
LCM(31080,31098) = ( 31080 × 31098) / 6
LCM(31080,31098) = 966525840 / 6
LCM(31080,31098) = 161087640

Least Common Multiple (LCM) of 31080 and 31098 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31080 and 31098. First we will calculate the prime factors of 31080 and 31098.

Prime Factorization of 31080

Prime Factorization of 31098

Now multiplying the highest exponent prime factors to calculate the LCM of 31080 and 31098.

LCM(31080,31098) = 2³ × 3¹ × 5¹ × 7¹ × 37¹ × 71¹ × 73¹
LCM(31080,31098) = 161087640