What is the Least Common Multiple of 48000 and 48007?

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 48000 and 48007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48000 and 48007, than apply into the LCM equation.

GCF(48000,48007) = 1
LCM(48000,48007) = ( 48000 × 48007) / 1
LCM(48000,48007) = 2304336000 / 1
LCM(48000,48007) = 2304336000

Least Common Multiple (LCM) of 48000 and 48007 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48000 and 48007. First we will calculate the prime factors of 48000 and 48007.

Prime Factorization of 48000

Prime Factorization of 48007

Now multiplying the highest exponent prime factors to calculate the LCM of 48000 and 48007.

LCM(48000,48007) = 2⁷ × 3¹ × 5³ × 61¹ × 787¹
LCM(48000,48007) = 2304336000