What is the Least Common Multiple of 2184 and 2196?

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 2184 and 2196 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2184 and 2196, than apply into the LCM equation.

GCF(2184,2196) = 12
LCM(2184,2196) = ( 2184 × 2196) / 12
LCM(2184,2196) = 4796064 / 12
LCM(2184,2196) = 399672

Least Common Multiple (LCM) of 2184 and 2196 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2184 and 2196. First we will calculate the prime factors of 2184 and 2196.

Prime Factorization of 2184

Prime Factorization of 2196

Now multiplying the highest exponent prime factors to calculate the LCM of 2184 and 2196.

LCM(2184,2196) = 2³ × 3² × 7¹ × 13¹ × 61¹
LCM(2184,2196) = 399672