What is the Least Common Multiple of 3096 and 3105?

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 3096 and 3105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3096 and 3105, than apply into the LCM equation.

GCF(3096,3105) = 9
LCM(3096,3105) = ( 3096 × 3105) / 9
LCM(3096,3105) = 9613080 / 9
LCM(3096,3105) = 1068120

Least Common Multiple (LCM) of 3096 and 3105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3096 and 3105. First we will calculate the prime factors of 3096 and 3105.

Prime Factorization of 3096

Prime Factorization of 3105

Now multiplying the highest exponent prime factors to calculate the LCM of 3096 and 3105.

LCM(3096,3105) = 2³ × 3³ × 43¹ × 5¹ × 23¹
LCM(3096,3105) = 1068120