What is the Least Common Multiple of 21438 and 21456?

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 21438 and 21456 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21438 and 21456, than apply into the LCM equation.

GCF(21438,21456) = 18
LCM(21438,21456) = ( 21438 × 21456) / 18
LCM(21438,21456) = 459973728 / 18
LCM(21438,21456) = 25554096

Least Common Multiple (LCM) of 21438 and 21456 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21438 and 21456. First we will calculate the prime factors of 21438 and 21456.

Prime Factorization of 21438

Prime Factorization of 21456

Now multiplying the highest exponent prime factors to calculate the LCM of 21438 and 21456.

LCM(21438,21456) = 2⁴ × 3³ × 397¹ × 149¹
LCM(21438,21456) = 25554096