What is the Least Common Multiple of 2800 and 2814?

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 2800 and 2814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2800 and 2814, than apply into the LCM equation.

GCF(2800,2814) = 14
LCM(2800,2814) = ( 2800 × 2814) / 14
LCM(2800,2814) = 7879200 / 14
LCM(2800,2814) = 562800

Least Common Multiple (LCM) of 2800 and 2814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2800 and 2814. First we will calculate the prime factors of 2800 and 2814.

Prime Factorization of 2800

Prime Factorization of 2814

Now multiplying the highest exponent prime factors to calculate the LCM of 2800 and 2814.

LCM(2800,2814) = 2⁴ × 5² × 7¹ × 3¹ × 67¹
LCM(2800,2814) = 562800