What is the Least Common Multiple of 21456 and 21460?

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 21456 and 21460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21456 and 21460, than apply into the LCM equation.

GCF(21456,21460) = 4
LCM(21456,21460) = ( 21456 × 21460) / 4
LCM(21456,21460) = 460445760 / 4
LCM(21456,21460) = 115111440

Least Common Multiple (LCM) of 21456 and 21460 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21456 and 21460. First we will calculate the prime factors of 21456 and 21460.

Prime Factorization of 21456

Prime Factorization of 21460

Now multiplying the highest exponent prime factors to calculate the LCM of 21456 and 21460.

LCM(21456,21460) = 2⁴ × 3² × 149¹ × 5¹ × 29¹ × 37¹
LCM(21456,21460) = 115111440