What is the Least Common Multiple of 10680 and 10700?

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 10680 and 10700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10680 and 10700, than apply into the LCM equation.

GCF(10680,10700) = 20
LCM(10680,10700) = ( 10680 × 10700) / 20
LCM(10680,10700) = 114276000 / 20
LCM(10680,10700) = 5713800

Least Common Multiple (LCM) of 10680 and 10700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10680 and 10700. First we will calculate the prime factors of 10680 and 10700.

Prime Factorization of 10680

Prime Factorization of 10700

Now multiplying the highest exponent prime factors to calculate the LCM of 10680 and 10700.

LCM(10680,10700) = 2³ × 3¹ × 5² × 89¹ × 107¹
LCM(10680,10700) = 5713800