What is the Least Common Multiple of 21780 and 21800?

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 21780 and 21800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21780 and 21800, than apply into the LCM equation.

GCF(21780,21800) = 20
LCM(21780,21800) = ( 21780 × 21800) / 20
LCM(21780,21800) = 474804000 / 20
LCM(21780,21800) = 23740200

Least Common Multiple (LCM) of 21780 and 21800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21780 and 21800. First we will calculate the prime factors of 21780 and 21800.

Prime Factorization of 21780

Prime Factorization of 21800

Now multiplying the highest exponent prime factors to calculate the LCM of 21780 and 21800.

LCM(21780,21800) = 2³ × 3² × 5² × 11² × 109¹
LCM(21780,21800) = 23740200