What is the Least Common Multiple of 1834 and 1854?

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 1834 and 1854 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1834 and 1854, than apply into the LCM equation.

GCF(1834,1854) = 2
LCM(1834,1854) = ( 1834 × 1854) / 2
LCM(1834,1854) = 3400236 / 2
LCM(1834,1854) = 1700118

Least Common Multiple (LCM) of 1834 and 1854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1834 and 1854. First we will calculate the prime factors of 1834 and 1854.

Prime Factorization of 1834

Prime Factorization of 1854

Now multiplying the highest exponent prime factors to calculate the LCM of 1834 and 1854.

LCM(1834,1854) = 2¹ × 7¹ × 131¹ × 3² × 103¹
LCM(1834,1854) = 1700118