What is the Least Common Multiple of 68000 and 68009?

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 68009 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 68009, than apply into the LCM equation.

GCF(68000,68009) = 1
LCM(68000,68009) = ( 68000 × 68009) / 1
LCM(68000,68009) = 4624612000 / 1
LCM(68000,68009) = 4624612000

Least Common Multiple (LCM) of 68000 and 68009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 68000 and 68009. First we will calculate the prime factors of 68000 and 68009.

Prime Factorization of 68000

Prime Factorization of 68009

Now multiplying the highest exponent prime factors to calculate the LCM of 68000 and 68009.

LCM(68000,68009) = 2⁵ × 5³ × 17¹ × 47¹ × 1447¹
LCM(68000,68009) = 4624612000