What is the Least Common Multiple of 40320 and 40338?

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 40338 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 40338, than apply into the LCM equation.

GCF(40320,40338) = 18
LCM(40320,40338) = ( 40320 × 40338) / 18
LCM(40320,40338) = 1626428160 / 18
LCM(40320,40338) = 90357120

Least Common Multiple (LCM) of 40320 and 40338 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40320 and 40338. First we will calculate the prime factors of 40320 and 40338.

Prime Factorization of 40320

Prime Factorization of 40338

Now multiplying the highest exponent prime factors to calculate the LCM of 40320 and 40338.

LCM(40320,40338) = 2⁷ × 3⁵ × 5¹ × 7¹ × 83¹
LCM(40320,40338) = 90357120