What is the Least Common Multiple of 21780 and 21792?

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 21792 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 21792, than apply into the LCM equation.

GCF(21780,21792) = 12
LCM(21780,21792) = ( 21780 × 21792) / 12
LCM(21780,21792) = 474629760 / 12
LCM(21780,21792) = 39552480

Least Common Multiple (LCM) of 21780 and 21792 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21780 and 21792. First we will calculate the prime factors of 21780 and 21792.

Prime Factorization of 21780

Prime Factorization of 21792

Now multiplying the highest exponent prime factors to calculate the LCM of 21780 and 21792.

LCM(21780,21792) = 2⁵ × 3² × 5¹ × 11² × 227¹
LCM(21780,21792) = 39552480