What is the Least Common Multiple of 6714 and 6723?

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 6714 and 6723 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6714 and 6723, than apply into the LCM equation.

GCF(6714,6723) = 9
LCM(6714,6723) = ( 6714 × 6723) / 9
LCM(6714,6723) = 45138222 / 9
LCM(6714,6723) = 5015358

Least Common Multiple (LCM) of 6714 and 6723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6714 and 6723. First we will calculate the prime factors of 6714 and 6723.

Prime Factorization of 6714

Prime Factorization of 6723

Now multiplying the highest exponent prime factors to calculate the LCM of 6714 and 6723.

LCM(6714,6723) = 2¹ × 3⁴ × 373¹ × 83¹
LCM(6714,6723) = 5015358