What is the Least Common Multiple of 1680 and 1694?

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 1680 and 1694 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1680 and 1694, than apply into the LCM equation.

GCF(1680,1694) = 14
LCM(1680,1694) = ( 1680 × 1694) / 14
LCM(1680,1694) = 2845920 / 14
LCM(1680,1694) = 203280

Least Common Multiple (LCM) of 1680 and 1694 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1694. First we will calculate the prime factors of 1680 and 1694.

Prime Factorization of 1680

Prime Factorization of 1694

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1694.

LCM(1680,1694) = 2⁴ × 3¹ × 5¹ × 7¹ × 11²
LCM(1680,1694) = 203280