What is the Least Common Multiple of 21174 and 21189?

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 21174 and 21189 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21174 and 21189, than apply into the LCM equation.

GCF(21174,21189) = 3
LCM(21174,21189) = ( 21174 × 21189) / 3
LCM(21174,21189) = 448655886 / 3
LCM(21174,21189) = 149551962

Least Common Multiple (LCM) of 21174 and 21189 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21174 and 21189. First we will calculate the prime factors of 21174 and 21189.

Prime Factorization of 21174

Prime Factorization of 21189

Now multiplying the highest exponent prime factors to calculate the LCM of 21174 and 21189.

LCM(21174,21189) = 2¹ × 3¹ × 3529¹ × 7¹ × 1009¹
LCM(21174,21189) = 149551962