What is the Least Common Multiple of 6300 and 6312?

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 6300 and 6312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6300 and 6312, than apply into the LCM equation.

GCF(6300,6312) = 12
LCM(6300,6312) = ( 6300 × 6312) / 12
LCM(6300,6312) = 39765600 / 12
LCM(6300,6312) = 3313800

Least Common Multiple (LCM) of 6300 and 6312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6300 and 6312. First we will calculate the prime factors of 6300 and 6312.

Prime Factorization of 6300

Prime Factorization of 6312

Now multiplying the highest exponent prime factors to calculate the LCM of 6300 and 6312.

LCM(6300,6312) = 2³ × 3² × 5² × 7¹ × 263¹
LCM(6300,6312) = 3313800