What is the Least Common Multiple of 1530 and 1545?

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 1530 and 1545 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1530 and 1545, than apply into the LCM equation.

GCF(1530,1545) = 15
LCM(1530,1545) = ( 1530 × 1545) / 15
LCM(1530,1545) = 2363850 / 15
LCM(1530,1545) = 157590

Least Common Multiple (LCM) of 1530 and 1545 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1530 and 1545. First we will calculate the prime factors of 1530 and 1545.

Prime Factorization of 1530

Prime Factorization of 1545

Now multiplying the highest exponent prime factors to calculate the LCM of 1530 and 1545.

LCM(1530,1545) = 2¹ × 3² × 5¹ × 17¹ × 103¹
LCM(1530,1545) = 157590