What is the Least Common Multiple of 13400 and 13408?

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 13400 and 13408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13400 and 13408, than apply into the LCM equation.

GCF(13400,13408) = 8
LCM(13400,13408) = ( 13400 × 13408) / 8
LCM(13400,13408) = 179667200 / 8
LCM(13400,13408) = 22458400

Least Common Multiple (LCM) of 13400 and 13408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13400 and 13408. First we will calculate the prime factors of 13400 and 13408.

Prime Factorization of 13400

Prime Factorization of 13408

Now multiplying the highest exponent prime factors to calculate the LCM of 13400 and 13408.

LCM(13400,13408) = 2⁵ × 5² × 67¹ × 419¹
LCM(13400,13408) = 22458400