What is the Least Common Multiple of 12270 and 12285?

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 12270 and 12285 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12270 and 12285, than apply into the LCM equation.

GCF(12270,12285) = 15
LCM(12270,12285) = ( 12270 × 12285) / 15
LCM(12270,12285) = 150736950 / 15
LCM(12270,12285) = 10049130

Least Common Multiple (LCM) of 12270 and 12285 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12270 and 12285. First we will calculate the prime factors of 12270 and 12285.

Prime Factorization of 12270

Prime Factorization of 12285

Now multiplying the highest exponent prime factors to calculate the LCM of 12270 and 12285.

LCM(12270,12285) = 2¹ × 3³ × 5¹ × 409¹ × 7¹ × 13¹
LCM(12270,12285) = 10049130