What is the Least Common Multiple of 67000 and 67014?

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 67000 and 67014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67000 and 67014, than apply into the LCM equation.

GCF(67000,67014) = 2
LCM(67000,67014) = ( 67000 × 67014) / 2
LCM(67000,67014) = 4489938000 / 2
LCM(67000,67014) = 2244969000

Least Common Multiple (LCM) of 67000 and 67014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67000 and 67014. First we will calculate the prime factors of 67000 and 67014.

Prime Factorization of 67000

Prime Factorization of 67014

Now multiplying the highest exponent prime factors to calculate the LCM of 67000 and 67014.

LCM(67000,67014) = 2³ × 5³ × 67¹ × 3³ × 17¹ × 73¹
LCM(67000,67014) = 2244969000