What is the Least Common Multiple of 1824 and 1830?

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 1830 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 1830, than apply into the LCM equation.

GCF(1824,1830) = 6
LCM(1824,1830) = ( 1824 × 1830) / 6
LCM(1824,1830) = 3337920 / 6
LCM(1824,1830) = 556320

Least Common Multiple (LCM) of 1824 and 1830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1824 and 1830. First we will calculate the prime factors of 1824 and 1830.

Prime Factorization of 1824

Prime Factorization of 1830

Now multiplying the highest exponent prime factors to calculate the LCM of 1824 and 1830.

LCM(1824,1830) = 2⁵ × 3¹ × 19¹ × 5¹ × 61¹
LCM(1824,1830) = 556320