What is the Least Common Multiple of 67983 and 68000?

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 67983 and 68000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67983 and 68000, than apply into the LCM equation.

GCF(67983,68000) = 17
LCM(67983,68000) = ( 67983 × 68000) / 17
LCM(67983,68000) = 4622844000 / 17
LCM(67983,68000) = 271932000

Least Common Multiple (LCM) of 67983 and 68000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67983 and 68000. First we will calculate the prime factors of 67983 and 68000.

Prime Factorization of 67983

Prime Factorization of 68000

Now multiplying the highest exponent prime factors to calculate the LCM of 67983 and 68000.

LCM(67983,68000) = 3¹ × 17¹ × 31¹ × 43¹ × 2⁵ × 5³
LCM(67983,68000) = 271932000