What is the Least Common Multiple of 21855 and 21870?

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 21855 and 21870 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21855 and 21870, than apply into the LCM equation.

GCF(21855,21870) = 15
LCM(21855,21870) = ( 21855 × 21870) / 15
LCM(21855,21870) = 477968850 / 15
LCM(21855,21870) = 31864590

Least Common Multiple (LCM) of 21855 and 21870 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21855 and 21870. First we will calculate the prime factors of 21855 and 21870.

Prime Factorization of 21855

Prime Factorization of 21870

Now multiplying the highest exponent prime factors to calculate the LCM of 21855 and 21870.

LCM(21855,21870) = 3⁷ × 5¹ × 31¹ × 47¹ × 2¹
LCM(21855,21870) = 31864590