What is the Least Common Multiple of 3900 and 3915?

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 3900 and 3915 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3900 and 3915, than apply into the LCM equation.

GCF(3900,3915) = 15
LCM(3900,3915) = ( 3900 × 3915) / 15
LCM(3900,3915) = 15268500 / 15
LCM(3900,3915) = 1017900

Least Common Multiple (LCM) of 3900 and 3915 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3900 and 3915. First we will calculate the prime factors of 3900 and 3915.

Prime Factorization of 3900

Prime Factorization of 3915

Now multiplying the highest exponent prime factors to calculate the LCM of 3900 and 3915.

LCM(3900,3915) = 2² × 3³ × 5² × 13¹ × 29¹
LCM(3900,3915) = 1017900