What is the Least Common Multiple of 30096 and 30107?

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 30096 and 30107 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30096 and 30107, than apply into the LCM equation.

GCF(30096,30107) = 11
LCM(30096,30107) = ( 30096 × 30107) / 11
LCM(30096,30107) = 906100272 / 11
LCM(30096,30107) = 82372752

Least Common Multiple (LCM) of 30096 and 30107 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30096 and 30107. First we will calculate the prime factors of 30096 and 30107.

Prime Factorization of 30096

Prime Factorization of 30107

Now multiplying the highest exponent prime factors to calculate the LCM of 30096 and 30107.

LCM(30096,30107) = 2⁴ × 3² × 11¹ × 19¹ × 7¹ × 17¹ × 23¹
LCM(30096,30107) = 82372752