What is the Least Common Multiple of 25000 and 25008?

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 25000 and 25008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25000 and 25008, than apply into the LCM equation.

GCF(25000,25008) = 8
LCM(25000,25008) = ( 25000 × 25008) / 8
LCM(25000,25008) = 625200000 / 8
LCM(25000,25008) = 78150000

Least Common Multiple (LCM) of 25000 and 25008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25000 and 25008. First we will calculate the prime factors of 25000 and 25008.

Prime Factorization of 25000

Prime Factorization of 25008

Now multiplying the highest exponent prime factors to calculate the LCM of 25000 and 25008.

LCM(25000,25008) = 2⁴ × 5⁵ × 3¹ × 521¹
LCM(25000,25008) = 78150000