What is the Least Common Multiple of 1578 and 1590?

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 1578 and 1590 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1578 and 1590, than apply into the LCM equation.

GCF(1578,1590) = 6
LCM(1578,1590) = ( 1578 × 1590) / 6
LCM(1578,1590) = 2509020 / 6
LCM(1578,1590) = 418170

Least Common Multiple (LCM) of 1578 and 1590 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1578 and 1590. First we will calculate the prime factors of 1578 and 1590.

Prime Factorization of 1578

Prime Factorization of 1590

Now multiplying the highest exponent prime factors to calculate the LCM of 1578 and 1590.

LCM(1578,1590) = 2¹ × 3¹ × 263¹ × 5¹ × 53¹
LCM(1578,1590) = 418170