What is the Least Common Multiple of 33996 and 34000?

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 33996 and 34000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33996 and 34000, than apply into the LCM equation.

GCF(33996,34000) = 4
LCM(33996,34000) = ( 33996 × 34000) / 4
LCM(33996,34000) = 1155864000 / 4
LCM(33996,34000) = 288966000

Least Common Multiple (LCM) of 33996 and 34000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33996 and 34000. First we will calculate the prime factors of 33996 and 34000.

Prime Factorization of 33996

Prime Factorization of 34000

Now multiplying the highest exponent prime factors to calculate the LCM of 33996 and 34000.

LCM(33996,34000) = 2⁴ × 3¹ × 2833¹ × 5³ × 17¹
LCM(33996,34000) = 288966000