What is the Least Common Multiple of 21000 and 21012?

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 21000 and 21012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21000 and 21012, than apply into the LCM equation.

GCF(21000,21012) = 12
LCM(21000,21012) = ( 21000 × 21012) / 12
LCM(21000,21012) = 441252000 / 12
LCM(21000,21012) = 36771000

Least Common Multiple (LCM) of 21000 and 21012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21000 and 21012. First we will calculate the prime factors of 21000 and 21012.

Prime Factorization of 21000

Prime Factorization of 21012

Now multiplying the highest exponent prime factors to calculate the LCM of 21000 and 21012.

LCM(21000,21012) = 2³ × 3¹ × 5³ × 7¹ × 17¹ × 103¹
LCM(21000,21012) = 36771000