What is the Least Common Multiple of 30999 and 31008?

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 30999 and 31008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30999 and 31008, than apply into the LCM equation.

GCF(30999,31008) = 3
LCM(30999,31008) = ( 30999 × 31008) / 3
LCM(30999,31008) = 961216992 / 3
LCM(30999,31008) = 320405664

Least Common Multiple (LCM) of 30999 and 31008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30999 and 31008. First we will calculate the prime factors of 30999 and 31008.

Prime Factorization of 30999

Prime Factorization of 31008

Now multiplying the highest exponent prime factors to calculate the LCM of 30999 and 31008.

LCM(30999,31008) = 3¹ × 10333¹ × 2⁵ × 17¹ × 19¹
LCM(30999,31008) = 320405664