What is the Least Common Multiple of 35000 and 35012?

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 35000 and 35012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35000 and 35012, than apply into the LCM equation.

GCF(35000,35012) = 4
LCM(35000,35012) = ( 35000 × 35012) / 4
LCM(35000,35012) = 1225420000 / 4
LCM(35000,35012) = 306355000

Least Common Multiple (LCM) of 35000 and 35012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 35000 and 35012. First we will calculate the prime factors of 35000 and 35012.

Prime Factorization of 35000

Prime Factorization of 35012

Now multiplying the highest exponent prime factors to calculate the LCM of 35000 and 35012.

LCM(35000,35012) = 2³ × 5⁴ × 7¹ × 8753¹
LCM(35000,35012) = 306355000