What is the Least Common Multiple of 64000 and 64008?

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 64000 and 64008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 64000 and 64008, than apply into the LCM equation.

GCF(64000,64008) = 8
LCM(64000,64008) = ( 64000 × 64008) / 8
LCM(64000,64008) = 4096512000 / 8
LCM(64000,64008) = 512064000

Least Common Multiple (LCM) of 64000 and 64008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 64000 and 64008. First we will calculate the prime factors of 64000 and 64008.

Prime Factorization of 64000

Prime Factorization of 64008

Now multiplying the highest exponent prime factors to calculate the LCM of 64000 and 64008.

LCM(64000,64008) = 2⁹ × 5³ × 3² × 7¹ × 127¹
LCM(64000,64008) = 512064000