What is the Least Common Multiple of 1803 and 1814?

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 1803 and 1814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1803 and 1814, than apply into the LCM equation.

GCF(1803,1814) = 1
LCM(1803,1814) = ( 1803 × 1814) / 1
LCM(1803,1814) = 3270642 / 1
LCM(1803,1814) = 3270642

Least Common Multiple (LCM) of 1803 and 1814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1803 and 1814. First we will calculate the prime factors of 1803 and 1814.

Prime Factorization of 1803

Prime Factorization of 1814

Now multiplying the highest exponent prime factors to calculate the LCM of 1803 and 1814.

LCM(1803,1814) = 3¹ × 601¹ × 2¹ × 907¹
LCM(1803,1814) = 3270642