What is the Least Common Multiple of 21720 and 21738?

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 21720 and 21738 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21720 and 21738, than apply into the LCM equation.

GCF(21720,21738) = 6
LCM(21720,21738) = ( 21720 × 21738) / 6
LCM(21720,21738) = 472149360 / 6
LCM(21720,21738) = 78691560

Least Common Multiple (LCM) of 21720 and 21738 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21720 and 21738. First we will calculate the prime factors of 21720 and 21738.

Prime Factorization of 21720

Prime Factorization of 21738

Now multiplying the highest exponent prime factors to calculate the LCM of 21720 and 21738.

LCM(21720,21738) = 2³ × 3¹ × 5¹ × 181¹ × 3623¹
LCM(21720,21738) = 78691560