What is the Least Common Multiple of 20400 and 20408?

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 20400 and 20408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20400 and 20408, than apply into the LCM equation.

GCF(20400,20408) = 8
LCM(20400,20408) = ( 20400 × 20408) / 8
LCM(20400,20408) = 416323200 / 8
LCM(20400,20408) = 52040400

Least Common Multiple (LCM) of 20400 and 20408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20400 and 20408. First we will calculate the prime factors of 20400 and 20408.

Prime Factorization of 20400

Prime Factorization of 20408

Now multiplying the highest exponent prime factors to calculate the LCM of 20400 and 20408.

LCM(20400,20408) = 2⁴ × 3¹ × 5² × 17¹ × 2551¹
LCM(20400,20408) = 52040400