What is the Least Common Multiple of 21114 and 21129?

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 21114 and 21129 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21114 and 21129, than apply into the LCM equation.

GCF(21114,21129) = 3
LCM(21114,21129) = ( 21114 × 21129) / 3
LCM(21114,21129) = 446117706 / 3
LCM(21114,21129) = 148705902

Least Common Multiple (LCM) of 21114 and 21129 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21114 and 21129. First we will calculate the prime factors of 21114 and 21129.

Prime Factorization of 21114

Prime Factorization of 21129

Now multiplying the highest exponent prime factors to calculate the LCM of 21114 and 21129.

LCM(21114,21129) = 2¹ × 3³ × 17¹ × 23¹ × 7043¹
LCM(21114,21129) = 148705902