What is the Least Common Multiple of 52000 and 52008?

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 52000 and 52008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 52000 and 52008, than apply into the LCM equation.

GCF(52000,52008) = 8
LCM(52000,52008) = ( 52000 × 52008) / 8
LCM(52000,52008) = 2704416000 / 8
LCM(52000,52008) = 338052000

Least Common Multiple (LCM) of 52000 and 52008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 52000 and 52008. First we will calculate the prime factors of 52000 and 52008.

Prime Factorization of 52000

Prime Factorization of 52008

Now multiplying the highest exponent prime factors to calculate the LCM of 52000 and 52008.

LCM(52000,52008) = 2⁵ × 5³ × 13¹ × 3¹ × 11¹ × 197¹
LCM(52000,52008) = 338052000