What is the Least Common Multiple of 1804 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 1804 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 1804 and 1824, than apply into the LCM equation.

GCF(1804,1824) = 4
LCM(1804,1824) = ( 1804 × 1824) / 4
LCM(1804,1824) = 3290496 / 4
LCM(1804,1824) = 822624

Least Common Multiple (LCM) of 1804 and 1824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1804 and 1824. First we will calculate the prime factors of 1804 and 1824.

Prime Factorization of 1804

Prime Factorization of 1824

Now multiplying the highest exponent prime factors to calculate the LCM of 1804 and 1824.

LCM(1804,1824) = 2⁵ × 11¹ × 41¹ × 3¹ × 19¹
LCM(1804,1824) = 822624