What is the Least Common Multiple of 31008 and 31014?

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 31008 and 31014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31008 and 31014, than apply into the LCM equation.

GCF(31008,31014) = 6
LCM(31008,31014) = ( 31008 × 31014) / 6
LCM(31008,31014) = 961682112 / 6
LCM(31008,31014) = 160280352

Least Common Multiple (LCM) of 31008 and 31014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31008 and 31014. First we will calculate the prime factors of 31008 and 31014.

Prime Factorization of 31008

Prime Factorization of 31014

Now multiplying the highest exponent prime factors to calculate the LCM of 31008 and 31014.

LCM(31008,31014) = 2⁵ × 3² × 17¹ × 19¹ × 1723¹
LCM(31008,31014) = 160280352