What is the Least Common Multiple of 21084 and 21100?

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 21084 and 21100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21084 and 21100, than apply into the LCM equation.

GCF(21084,21100) = 4
LCM(21084,21100) = ( 21084 × 21100) / 4
LCM(21084,21100) = 444872400 / 4
LCM(21084,21100) = 111218100

Least Common Multiple (LCM) of 21084 and 21100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21084 and 21100. First we will calculate the prime factors of 21084 and 21100.

Prime Factorization of 21084

Prime Factorization of 21100

Now multiplying the highest exponent prime factors to calculate the LCM of 21084 and 21100.

LCM(21084,21100) = 2² × 3¹ × 7¹ × 251¹ × 5² × 211¹
LCM(21084,21100) = 111218100