What is the Least Common Multiple of 1809 and 1824?

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 1809 and 1824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1809 and 1824, than apply into the LCM equation.

GCF(1809,1824) = 3
LCM(1809,1824) = ( 1809 × 1824) / 3
LCM(1809,1824) = 3299616 / 3
LCM(1809,1824) = 1099872

Least Common Multiple (LCM) of 1809 and 1824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1809 and 1824. First we will calculate the prime factors of 1809 and 1824.

Prime Factorization of 1809

Prime Factorization of 1824

Now multiplying the highest exponent prime factors to calculate the LCM of 1809 and 1824.

LCM(1809,1824) = 3³ × 67¹ × 2⁵ × 19¹
LCM(1809,1824) = 1099872