What is the Least Common Multiple of 2400 and 2408?

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 2400 and 2408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2400 and 2408, than apply into the LCM equation.

GCF(2400,2408) = 8
LCM(2400,2408) = ( 2400 × 2408) / 8
LCM(2400,2408) = 5779200 / 8
LCM(2400,2408) = 722400

Least Common Multiple (LCM) of 2400 and 2408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2400 and 2408. First we will calculate the prime factors of 2400 and 2408.

Prime Factorization of 2400

Prime Factorization of 2408

Now multiplying the highest exponent prime factors to calculate the LCM of 2400 and 2408.

LCM(2400,2408) = 2⁵ × 3¹ × 5² × 7¹ × 43¹
LCM(2400,2408) = 722400