What is the Least Common Multiple of 3105 and 3120?

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 3105 and 3120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3105 and 3120, than apply into the LCM equation.

GCF(3105,3120) = 15
LCM(3105,3120) = ( 3105 × 3120) / 15
LCM(3105,3120) = 9687600 / 15
LCM(3105,3120) = 645840

Least Common Multiple (LCM) of 3105 and 3120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3105 and 3120. First we will calculate the prime factors of 3105 and 3120.

Prime Factorization of 3105

Prime Factorization of 3120

Now multiplying the highest exponent prime factors to calculate the LCM of 3105 and 3120.

LCM(3105,3120) = 3³ × 5¹ × 23¹ × 2⁴ × 13¹
LCM(3105,3120) = 645840