What is the Least Common Multiple of 1674 and 1683?

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 1674 and 1683 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1674 and 1683, than apply into the LCM equation.

GCF(1674,1683) = 9
LCM(1674,1683) = ( 1674 × 1683) / 9
LCM(1674,1683) = 2817342 / 9
LCM(1674,1683) = 313038

Least Common Multiple (LCM) of 1674 and 1683 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1674 and 1683. First we will calculate the prime factors of 1674 and 1683.

Prime Factorization of 1674

Prime Factorization of 1683

Now multiplying the highest exponent prime factors to calculate the LCM of 1674 and 1683.

LCM(1674,1683) = 2¹ × 3³ × 31¹ × 11¹ × 17¹
LCM(1674,1683) = 313038