What is the Least Common Multiple of 1215 and 1230?

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 1215 and 1230 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1215 and 1230, than apply into the LCM equation.

GCF(1215,1230) = 15
LCM(1215,1230) = ( 1215 × 1230) / 15
LCM(1215,1230) = 1494450 / 15
LCM(1215,1230) = 99630

Least Common Multiple (LCM) of 1215 and 1230 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1215 and 1230. First we will calculate the prime factors of 1215 and 1230.

Prime Factorization of 1215

Prime Factorization of 1230

Now multiplying the highest exponent prime factors to calculate the LCM of 1215 and 1230.

LCM(1215,1230) = 3⁵ × 5¹ × 2¹ × 41¹
LCM(1215,1230) = 99630