What is the Least Common Multiple of 1824 and 1836?

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 1824 and 1836 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1824 and 1836, than apply into the LCM equation.

GCF(1824,1836) = 12
LCM(1824,1836) = ( 1824 × 1836) / 12
LCM(1824,1836) = 3348864 / 12
LCM(1824,1836) = 279072

Least Common Multiple (LCM) of 1824 and 1836 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1824 and 1836. First we will calculate the prime factors of 1824 and 1836.

Prime Factorization of 1824

Prime Factorization of 1836

Now multiplying the highest exponent prime factors to calculate the LCM of 1824 and 1836.

LCM(1824,1836) = 2⁵ × 3³ × 19¹ × 17¹
LCM(1824,1836) = 279072