What is the Least Common Multiple of 1689 and 1708?

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 1689 and 1708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1689 and 1708, than apply into the LCM equation.

GCF(1689,1708) = 1
LCM(1689,1708) = ( 1689 × 1708) / 1
LCM(1689,1708) = 2884812 / 1
LCM(1689,1708) = 2884812

Least Common Multiple (LCM) of 1689 and 1708 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1689 and 1708. First we will calculate the prime factors of 1689 and 1708.

Prime Factorization of 1689

Prime Factorization of 1708

Now multiplying the highest exponent prime factors to calculate the LCM of 1689 and 1708.

LCM(1689,1708) = 3¹ × 563¹ × 2² × 7¹ × 61¹
LCM(1689,1708) = 2884812