What is the Least Common Multiple of 2080 and 2100?

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 2080 and 2100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2080 and 2100, than apply into the LCM equation.

GCF(2080,2100) = 20
LCM(2080,2100) = ( 2080 × 2100) / 20
LCM(2080,2100) = 4368000 / 20
LCM(2080,2100) = 218400

Least Common Multiple (LCM) of 2080 and 2100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2080 and 2100. First we will calculate the prime factors of 2080 and 2100.

Prime Factorization of 2080

Prime Factorization of 2100

Now multiplying the highest exponent prime factors to calculate the LCM of 2080 and 2100.

LCM(2080,2100) = 2⁵ × 5² × 13¹ × 3¹ × 7¹
LCM(2080,2100) = 218400