What is the Least Common Multiple of 56000 and 56008?

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 56000 and 56008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 56000 and 56008, than apply into the LCM equation.

GCF(56000,56008) = 8
LCM(56000,56008) = ( 56000 × 56008) / 8
LCM(56000,56008) = 3136448000 / 8
LCM(56000,56008) = 392056000

Least Common Multiple (LCM) of 56000 and 56008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 56000 and 56008. First we will calculate the prime factors of 56000 and 56008.

Prime Factorization of 56000

Prime Factorization of 56008

Now multiplying the highest exponent prime factors to calculate the LCM of 56000 and 56008.

LCM(56000,56008) = 2⁶ × 5³ × 7¹ × 7001¹
LCM(56000,56008) = 392056000