What is the Least Common Multiple of 13800 and 13813?

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 13800 and 13813 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13800 and 13813, than apply into the LCM equation.

GCF(13800,13813) = 1
LCM(13800,13813) = ( 13800 × 13813) / 1
LCM(13800,13813) = 190619400 / 1
LCM(13800,13813) = 190619400

Least Common Multiple (LCM) of 13800 and 13813 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13800 and 13813. First we will calculate the prime factors of 13800 and 13813.

Prime Factorization of 13800

Prime Factorization of 13813

Now multiplying the highest exponent prime factors to calculate the LCM of 13800 and 13813.

LCM(13800,13813) = 2³ × 3¹ × 5² × 23¹ × 19¹ × 727¹
LCM(13800,13813) = 190619400