What is the Least Common Multiple of 13800 and 13820?

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 13820 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 13820, than apply into the LCM equation.

GCF(13800,13820) = 20
LCM(13800,13820) = ( 13800 × 13820) / 20
LCM(13800,13820) = 190716000 / 20
LCM(13800,13820) = 9535800

Least Common Multiple (LCM) of 13800 and 13820 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13800 and 13820. First we will calculate the prime factors of 13800 and 13820.

Prime Factorization of 13800

Prime Factorization of 13820

Now multiplying the highest exponent prime factors to calculate the LCM of 13800 and 13820.

LCM(13800,13820) = 2³ × 3¹ × 5² × 23¹ × 691¹
LCM(13800,13820) = 9535800