What is the Least Common Multiple of 21360 and 21369?

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 21360 and 21369 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21360 and 21369, than apply into the LCM equation.

GCF(21360,21369) = 3
LCM(21360,21369) = ( 21360 × 21369) / 3
LCM(21360,21369) = 456441840 / 3
LCM(21360,21369) = 152147280

Least Common Multiple (LCM) of 21360 and 21369 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21360 and 21369. First we will calculate the prime factors of 21360 and 21369.

Prime Factorization of 21360

Prime Factorization of 21369

Now multiplying the highest exponent prime factors to calculate the LCM of 21360 and 21369.

LCM(21360,21369) = 2⁴ × 3¹ × 5¹ × 89¹ × 17¹ × 419¹
LCM(21360,21369) = 152147280