What is the Least Common Multiple of 10400 and 10419?

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 10419 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 10419, than apply into the LCM equation.

GCF(10400,10419) = 1
LCM(10400,10419) = ( 10400 × 10419) / 1
LCM(10400,10419) = 108357600 / 1
LCM(10400,10419) = 108357600

Least Common Multiple (LCM) of 10400 and 10419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10400 and 10419. First we will calculate the prime factors of 10400 and 10419.

Prime Factorization of 10400

Prime Factorization of 10419

Now multiplying the highest exponent prime factors to calculate the LCM of 10400 and 10419.

LCM(10400,10419) = 2⁵ × 5² × 13¹ × 3¹ × 23¹ × 151¹
LCM(10400,10419) = 108357600