What is the Least Common Multiple of 1209 and 1222?

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 1209 and 1222 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1209 and 1222, than apply into the LCM equation.

GCF(1209,1222) = 13
LCM(1209,1222) = ( 1209 × 1222) / 13
LCM(1209,1222) = 1477398 / 13
LCM(1209,1222) = 113646

Least Common Multiple (LCM) of 1209 and 1222 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1209 and 1222. First we will calculate the prime factors of 1209 and 1222.

Prime Factorization of 1209

Prime Factorization of 1222

Now multiplying the highest exponent prime factors to calculate the LCM of 1209 and 1222.

LCM(1209,1222) = 3¹ × 13¹ × 31¹ × 2¹ × 47¹
LCM(1209,1222) = 113646