What is the Least Common Multiple of 5680 and 5700?

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 5680 and 5700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5680 and 5700, than apply into the LCM equation.

GCF(5680,5700) = 20
LCM(5680,5700) = ( 5680 × 5700) / 20
LCM(5680,5700) = 32376000 / 20
LCM(5680,5700) = 1618800

Least Common Multiple (LCM) of 5680 and 5700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5680 and 5700. First we will calculate the prime factors of 5680 and 5700.

Prime Factorization of 5680

Prime Factorization of 5700

Now multiplying the highest exponent prime factors to calculate the LCM of 5680 and 5700.

LCM(5680,5700) = 2⁴ × 5² × 71¹ × 3¹ × 19¹
LCM(5680,5700) = 1618800