What is the Least Common Multiple of 21264 and 21270?

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 21264 and 21270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21264 and 21270, than apply into the LCM equation.

GCF(21264,21270) = 6
LCM(21264,21270) = ( 21264 × 21270) / 6
LCM(21264,21270) = 452285280 / 6
LCM(21264,21270) = 75380880

Least Common Multiple (LCM) of 21264 and 21270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21264 and 21270. First we will calculate the prime factors of 21264 and 21270.

Prime Factorization of 21264

Prime Factorization of 21270

Now multiplying the highest exponent prime factors to calculate the LCM of 21264 and 21270.

LCM(21264,21270) = 2⁴ × 3¹ × 443¹ × 5¹ × 709¹
LCM(21264,21270) = 75380880