What is the Least Common Multiple of 1700 and 1714?

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 1700 and 1714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1700 and 1714, than apply into the LCM equation.

GCF(1700,1714) = 2
LCM(1700,1714) = ( 1700 × 1714) / 2
LCM(1700,1714) = 2913800 / 2
LCM(1700,1714) = 1456900

Least Common Multiple (LCM) of 1700 and 1714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1700 and 1714. First we will calculate the prime factors of 1700 and 1714.

Prime Factorization of 1700

Prime Factorization of 1714

Now multiplying the highest exponent prime factors to calculate the LCM of 1700 and 1714.

LCM(1700,1714) = 2² × 5² × 17¹ × 857¹
LCM(1700,1714) = 1456900