What is the Least Common Multiple of 6300 and 6309?

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 6309 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 6309, than apply into the LCM equation.

GCF(6300,6309) = 9
LCM(6300,6309) = ( 6300 × 6309) / 9
LCM(6300,6309) = 39746700 / 9
LCM(6300,6309) = 4416300

Least Common Multiple (LCM) of 6300 and 6309 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6300 and 6309. First we will calculate the prime factors of 6300 and 6309.

Prime Factorization of 6300

Prime Factorization of 6309

Now multiplying the highest exponent prime factors to calculate the LCM of 6300 and 6309.

LCM(6300,6309) = 2² × 3² × 5² × 7¹ × 701¹
LCM(6300,6309) = 4416300