What is the Least Common Multiple of 1563 and 1578?

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 1563 and 1578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1563 and 1578, than apply into the LCM equation.

GCF(1563,1578) = 3
LCM(1563,1578) = ( 1563 × 1578) / 3
LCM(1563,1578) = 2466414 / 3
LCM(1563,1578) = 822138

Least Common Multiple (LCM) of 1563 and 1578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1563 and 1578. First we will calculate the prime factors of 1563 and 1578.

Prime Factorization of 1563

Prime Factorization of 1578

Now multiplying the highest exponent prime factors to calculate the LCM of 1563 and 1578.

LCM(1563,1578) = 3¹ × 521¹ × 2¹ × 263¹
LCM(1563,1578) = 822138