What is the Least Common Multiple of 74000 and 74016?

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 74000 and 74016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74000 and 74016, than apply into the LCM equation.

GCF(74000,74016) = 16
LCM(74000,74016) = ( 74000 × 74016) / 16
LCM(74000,74016) = 5477184000 / 16
LCM(74000,74016) = 342324000

Least Common Multiple (LCM) of 74000 and 74016 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74000 and 74016. First we will calculate the prime factors of 74000 and 74016.

Prime Factorization of 74000

Prime Factorization of 74016

Now multiplying the highest exponent prime factors to calculate the LCM of 74000 and 74016.

LCM(74000,74016) = 2⁵ × 5³ × 37¹ × 3² × 257¹
LCM(74000,74016) = 342324000