What is the Least Common Multiple of 38100 and 38115?

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 38100 and 38115 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38100 and 38115, than apply into the LCM equation.

GCF(38100,38115) = 15
LCM(38100,38115) = ( 38100 × 38115) / 15
LCM(38100,38115) = 1452181500 / 15
LCM(38100,38115) = 96812100

Least Common Multiple (LCM) of 38100 and 38115 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38100 and 38115. First we will calculate the prime factors of 38100 and 38115.

Prime Factorization of 38100

Prime Factorization of 38115

Now multiplying the highest exponent prime factors to calculate the LCM of 38100 and 38115.

LCM(38100,38115) = 2² × 3² × 5² × 127¹ × 7¹ × 11²
LCM(38100,38115) = 96812100