What is the Least Common Multiple of 1680 and 1689?

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 1689 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 1689, than apply into the LCM equation.

GCF(1680,1689) = 3
LCM(1680,1689) = ( 1680 × 1689) / 3
LCM(1680,1689) = 2837520 / 3
LCM(1680,1689) = 945840

Least Common Multiple (LCM) of 1680 and 1689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1680 and 1689. First we will calculate the prime factors of 1680 and 1689.

Prime Factorization of 1680

Prime Factorization of 1689

Now multiplying the highest exponent prime factors to calculate the LCM of 1680 and 1689.

LCM(1680,1689) = 2⁴ × 3¹ × 5¹ × 7¹ × 563¹
LCM(1680,1689) = 945840