What is the Least Common Multiple of 1545 and 1564?

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 1545 and 1564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1545 and 1564, than apply into the LCM equation.

GCF(1545,1564) = 1
LCM(1545,1564) = ( 1545 × 1564) / 1
LCM(1545,1564) = 2416380 / 1
LCM(1545,1564) = 2416380

Least Common Multiple (LCM) of 1545 and 1564 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1545 and 1564. First we will calculate the prime factors of 1545 and 1564.

Prime Factorization of 1545

Prime Factorization of 1564

Now multiplying the highest exponent prime factors to calculate the LCM of 1545 and 1564.

LCM(1545,1564) = 3¹ × 5¹ × 103¹ × 2² × 17¹ × 23¹
LCM(1545,1564) = 2416380