What is the Least Common Multiple of 21129 and 21138?

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 21129 and 21138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21129 and 21138, than apply into the LCM equation.

GCF(21129,21138) = 3
LCM(21129,21138) = ( 21129 × 21138) / 3
LCM(21129,21138) = 446624802 / 3
LCM(21129,21138) = 148874934

Least Common Multiple (LCM) of 21129 and 21138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21129 and 21138. First we will calculate the prime factors of 21129 and 21138.

Prime Factorization of 21129

Prime Factorization of 21138

Now multiplying the highest exponent prime factors to calculate the LCM of 21129 and 21138.

LCM(21129,21138) = 3¹ × 7043¹ × 2¹ × 13¹ × 271¹
LCM(21129,21138) = 148874934