What is the Least Common Multiple of 12030 and 12045?

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 12030 and 12045 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12030 and 12045, than apply into the LCM equation.

GCF(12030,12045) = 15
LCM(12030,12045) = ( 12030 × 12045) / 15
LCM(12030,12045) = 144901350 / 15
LCM(12030,12045) = 9660090

Least Common Multiple (LCM) of 12030 and 12045 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12030 and 12045. First we will calculate the prime factors of 12030 and 12045.

Prime Factorization of 12030

Prime Factorization of 12045

Now multiplying the highest exponent prime factors to calculate the LCM of 12030 and 12045.

LCM(12030,12045) = 2¹ × 3¹ × 5¹ × 401¹ × 11¹ × 73¹
LCM(12030,12045) = 9660090