What is the Least Common Multiple of 1214 and 1232?

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 1214 and 1232 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1214 and 1232, than apply into the LCM equation.

GCF(1214,1232) = 2
LCM(1214,1232) = ( 1214 × 1232) / 2
LCM(1214,1232) = 1495648 / 2
LCM(1214,1232) = 747824

Least Common Multiple (LCM) of 1214 and 1232 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1214 and 1232. First we will calculate the prime factors of 1214 and 1232.

Prime Factorization of 1214

Prime Factorization of 1232

Now multiplying the highest exponent prime factors to calculate the LCM of 1214 and 1232.

LCM(1214,1232) = 2⁴ × 607¹ × 7¹ × 11¹
LCM(1214,1232) = 747824