What is the Least Common Multiple of 6700 and 6714?

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 6700 and 6714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6700 and 6714, than apply into the LCM equation.

GCF(6700,6714) = 2
LCM(6700,6714) = ( 6700 × 6714) / 2
LCM(6700,6714) = 44983800 / 2
LCM(6700,6714) = 22491900

Least Common Multiple (LCM) of 6700 and 6714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6700 and 6714. First we will calculate the prime factors of 6700 and 6714.

Prime Factorization of 6700

Prime Factorization of 6714

Now multiplying the highest exponent prime factors to calculate the LCM of 6700 and 6714.

LCM(6700,6714) = 2² × 5² × 67¹ × 3² × 373¹
LCM(6700,6714) = 22491900