What is the Least Common Multiple of 52000 and 52014?

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 52014 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 52014, than apply into the LCM equation.

GCF(52000,52014) = 2
LCM(52000,52014) = ( 52000 × 52014) / 2
LCM(52000,52014) = 2704728000 / 2
LCM(52000,52014) = 1352364000

Least Common Multiple (LCM) of 52000 and 52014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 52000 and 52014. First we will calculate the prime factors of 52000 and 52014.

Prime Factorization of 52000

Prime Factorization of 52014

Now multiplying the highest exponent prime factors to calculate the LCM of 52000 and 52014.

LCM(52000,52014) = 2⁵ × 5³ × 13¹ × 3¹ × 8669¹
LCM(52000,52014) = 1352364000