What is the Least Common Multiple of 71700 and 71712?

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 71700 and 71712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71700 and 71712, than apply into the LCM equation.

GCF(71700,71712) = 12
LCM(71700,71712) = ( 71700 × 71712) / 12
LCM(71700,71712) = 5141750400 / 12
LCM(71700,71712) = 428479200

Least Common Multiple (LCM) of 71700 and 71712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71700 and 71712. First we will calculate the prime factors of 71700 and 71712.

Prime Factorization of 71700

Prime Factorization of 71712

Now multiplying the highest exponent prime factors to calculate the LCM of 71700 and 71712.

LCM(71700,71712) = 2⁵ × 3³ × 5² × 239¹ × 83¹
LCM(71700,71712) = 428479200