What is the Least Common Multiple of 33705 and 33714?

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 33705 and 33714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33705 and 33714, than apply into the LCM equation.

GCF(33705,33714) = 9
LCM(33705,33714) = ( 33705 × 33714) / 9
LCM(33705,33714) = 1136330370 / 9
LCM(33705,33714) = 126258930

Least Common Multiple (LCM) of 33705 and 33714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33705 and 33714. First we will calculate the prime factors of 33705 and 33714.

Prime Factorization of 33705

Prime Factorization of 33714

Now multiplying the highest exponent prime factors to calculate the LCM of 33705 and 33714.

LCM(33705,33714) = 3² × 5¹ × 7¹ × 107¹ × 2¹ × 1873¹
LCM(33705,33714) = 126258930