What is the Least Common Multiple of 21105 and 21114?

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 21105 and 21114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21105 and 21114, than apply into the LCM equation.

GCF(21105,21114) = 9
LCM(21105,21114) = ( 21105 × 21114) / 9
LCM(21105,21114) = 445610970 / 9
LCM(21105,21114) = 49512330

Least Common Multiple (LCM) of 21105 and 21114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21105 and 21114. First we will calculate the prime factors of 21105 and 21114.

Prime Factorization of 21105

Prime Factorization of 21114

Now multiplying the highest exponent prime factors to calculate the LCM of 21105 and 21114.

LCM(21105,21114) = 3³ × 5¹ × 7¹ × 67¹ × 2¹ × 17¹ × 23¹
LCM(21105,21114) = 49512330