What is the Least Common Multiple of 40320 and 40335?

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 40320 and 40335 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40320 and 40335, than apply into the LCM equation.

GCF(40320,40335) = 15
LCM(40320,40335) = ( 40320 × 40335) / 15
LCM(40320,40335) = 1626307200 / 15
LCM(40320,40335) = 108420480

Least Common Multiple (LCM) of 40320 and 40335 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40320 and 40335. First we will calculate the prime factors of 40320 and 40335.

Prime Factorization of 40320

Prime Factorization of 40335

Now multiplying the highest exponent prime factors to calculate the LCM of 40320 and 40335.

LCM(40320,40335) = 2⁷ × 3² × 5¹ × 7¹ × 2689¹
LCM(40320,40335) = 108420480