What is the Least Common Multiple of 1821 and 1840?

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 1821 and 1840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1821 and 1840, than apply into the LCM equation.

GCF(1821,1840) = 1
LCM(1821,1840) = ( 1821 × 1840) / 1
LCM(1821,1840) = 3350640 / 1
LCM(1821,1840) = 3350640

Least Common Multiple (LCM) of 1821 and 1840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1821 and 1840. First we will calculate the prime factors of 1821 and 1840.

Prime Factorization of 1821

Prime Factorization of 1840

Now multiplying the highest exponent prime factors to calculate the LCM of 1821 and 1840.

LCM(1821,1840) = 3¹ × 607¹ × 2⁴ × 5¹ × 23¹
LCM(1821,1840) = 3350640