What is the Least Common Multiple of 1205 and 1224?

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 1205 and 1224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1205 and 1224, than apply into the LCM equation.

GCF(1205,1224) = 1
LCM(1205,1224) = ( 1205 × 1224) / 1
LCM(1205,1224) = 1474920 / 1
LCM(1205,1224) = 1474920

Least Common Multiple (LCM) of 1205 and 1224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1205 and 1224. First we will calculate the prime factors of 1205 and 1224.

Prime Factorization of 1205

Prime Factorization of 1224

Now multiplying the highest exponent prime factors to calculate the LCM of 1205 and 1224.

LCM(1205,1224) = 5¹ × 241¹ × 2³ × 3² × 17¹
LCM(1205,1224) = 1474920