What is the Least Common Multiple of 30800 and 30814?

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 30800 and 30814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30800 and 30814, than apply into the LCM equation.

GCF(30800,30814) = 14
LCM(30800,30814) = ( 30800 × 30814) / 14
LCM(30800,30814) = 949071200 / 14
LCM(30800,30814) = 67790800

Least Common Multiple (LCM) of 30800 and 30814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30800 and 30814. First we will calculate the prime factors of 30800 and 30814.

Prime Factorization of 30800

Prime Factorization of 30814

Now multiplying the highest exponent prime factors to calculate the LCM of 30800 and 30814.

LCM(30800,30814) = 2⁴ × 5² × 7¹ × 11¹ × 31¹ × 71¹
LCM(30800,30814) = 67790800