What is the Least Common Multiple of 1230 and 1245?

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 1230 and 1245 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1230 and 1245, than apply into the LCM equation.

GCF(1230,1245) = 15
LCM(1230,1245) = ( 1230 × 1245) / 15
LCM(1230,1245) = 1531350 / 15
LCM(1230,1245) = 102090

Least Common Multiple (LCM) of 1230 and 1245 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1230 and 1245. First we will calculate the prime factors of 1230 and 1245.

Prime Factorization of 1230

Prime Factorization of 1245

Now multiplying the highest exponent prime factors to calculate the LCM of 1230 and 1245.

LCM(1230,1245) = 2¹ × 3¹ × 5¹ × 41¹ × 83¹
LCM(1230,1245) = 102090