What is the Least Common Multiple of 21390 and 21408?

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 21390 and 21408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21390 and 21408, than apply into the LCM equation.

GCF(21390,21408) = 6
LCM(21390,21408) = ( 21390 × 21408) / 6
LCM(21390,21408) = 457917120 / 6
LCM(21390,21408) = 76319520

Least Common Multiple (LCM) of 21390 and 21408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21390 and 21408. First we will calculate the prime factors of 21390 and 21408.

Prime Factorization of 21390

Prime Factorization of 21408

Now multiplying the highest exponent prime factors to calculate the LCM of 21390 and 21408.

LCM(21390,21408) = 2⁵ × 3¹ × 5¹ × 23¹ × 31¹ × 223¹
LCM(21390,21408) = 76319520