What is the Least Common Multiple of 10400 and 10405?

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 10400 and 10405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10400 and 10405, than apply into the LCM equation.

GCF(10400,10405) = 5
LCM(10400,10405) = ( 10400 × 10405) / 5
LCM(10400,10405) = 108212000 / 5
LCM(10400,10405) = 21642400

Least Common Multiple (LCM) of 10400 and 10405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10400 and 10405. First we will calculate the prime factors of 10400 and 10405.

Prime Factorization of 10400

Prime Factorization of 10405

Now multiplying the highest exponent prime factors to calculate the LCM of 10400 and 10405.

LCM(10400,10405) = 2⁵ × 5² × 13¹ × 2081¹
LCM(10400,10405) = 21642400