What is the Least Common Multiple of 10800 and 10820?

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 10800 and 10820 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10800 and 10820, than apply into the LCM equation.

GCF(10800,10820) = 20
LCM(10800,10820) = ( 10800 × 10820) / 20
LCM(10800,10820) = 116856000 / 20
LCM(10800,10820) = 5842800

Least Common Multiple (LCM) of 10800 and 10820 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10800 and 10820. First we will calculate the prime factors of 10800 and 10820.

Prime Factorization of 10800

Prime Factorization of 10820

Now multiplying the highest exponent prime factors to calculate the LCM of 10800 and 10820.

LCM(10800,10820) = 2⁴ × 3³ × 5² × 541¹
LCM(10800,10820) = 5842800