What is the Least Common Multiple of 21870 and 21889?

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 21870 and 21889 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21870 and 21889, than apply into the LCM equation.

GCF(21870,21889) = 1
LCM(21870,21889) = ( 21870 × 21889) / 1
LCM(21870,21889) = 478712430 / 1
LCM(21870,21889) = 478712430

Least Common Multiple (LCM) of 21870 and 21889 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21870 and 21889. First we will calculate the prime factors of 21870 and 21889.

Prime Factorization of 21870

Prime Factorization of 21889

Now multiplying the highest exponent prime factors to calculate the LCM of 21870 and 21889.

LCM(21870,21889) = 2¹ × 3⁷ × 5¹ × 7¹ × 53¹ × 59¹
LCM(21870,21889) = 478712430