What is the Least Common Multiple of 30840 and 30854?

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 30840 and 30854 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30840 and 30854, than apply into the LCM equation.

GCF(30840,30854) = 2
LCM(30840,30854) = ( 30840 × 30854) / 2
LCM(30840,30854) = 951537360 / 2
LCM(30840,30854) = 475768680

Least Common Multiple (LCM) of 30840 and 30854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30840 and 30854. First we will calculate the prime factors of 30840 and 30854.

Prime Factorization of 30840

Prime Factorization of 30854

Now multiplying the highest exponent prime factors to calculate the LCM of 30840 and 30854.

LCM(30840,30854) = 2³ × 3¹ × 5¹ × 257¹ × 15427¹
LCM(30840,30854) = 475768680