What is the Least Common Multiple of 1665 and 1674?

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 1665 and 1674 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1665 and 1674, than apply into the LCM equation.

GCF(1665,1674) = 9
LCM(1665,1674) = ( 1665 × 1674) / 9
LCM(1665,1674) = 2787210 / 9
LCM(1665,1674) = 309690

Least Common Multiple (LCM) of 1665 and 1674 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1665 and 1674. First we will calculate the prime factors of 1665 and 1674.

Prime Factorization of 1665

Prime Factorization of 1674

Now multiplying the highest exponent prime factors to calculate the LCM of 1665 and 1674.

LCM(1665,1674) = 3³ × 5¹ × 37¹ × 2¹ × 31¹
LCM(1665,1674) = 309690