What is the Least Common Multiple of 5700 and 5712?

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 5700 and 5712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5700 and 5712, than apply into the LCM equation.

GCF(5700,5712) = 12
LCM(5700,5712) = ( 5700 × 5712) / 12
LCM(5700,5712) = 32558400 / 12
LCM(5700,5712) = 2713200

Least Common Multiple (LCM) of 5700 and 5712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5700 and 5712. First we will calculate the prime factors of 5700 and 5712.

Prime Factorization of 5700

Prime Factorization of 5712

Now multiplying the highest exponent prime factors to calculate the LCM of 5700 and 5712.

LCM(5700,5712) = 2⁴ × 3¹ × 5² × 19¹ × 7¹ × 17¹
LCM(5700,5712) = 2713200