What is the Least Common Multiple of 68000 and 68014?

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 68000 and 68014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68000 and 68014, than apply into the LCM equation.

GCF(68000,68014) = 2
LCM(68000,68014) = ( 68000 × 68014) / 2
LCM(68000,68014) = 4624952000 / 2
LCM(68000,68014) = 2312476000

Least Common Multiple (LCM) of 68000 and 68014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 68000 and 68014. First we will calculate the prime factors of 68000 and 68014.

Prime Factorization of 68000

Prime Factorization of 68014

Now multiplying the highest exponent prime factors to calculate the LCM of 68000 and 68014.

LCM(68000,68014) = 2⁵ × 5³ × 17¹ × 31¹ × 1097¹
LCM(68000,68014) = 2312476000