GCF and LCM Calculator Logo

What is the Least Common Multiple of 31200 and 31217?

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 (LCM) of 31200 and 31217 is 973970400.

LCM(31200,31217) = 973970400

LCM Calculator and
and

Least Common Multiple of 31200 and 31217 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31200 and 31217, than apply into the LCM equation.

GCF(31200,31217) = 1
LCM(31200,31217) = ( 31200 × 31217) / 1
LCM(31200,31217) = 973970400 / 1
LCM(31200,31217) = 973970400

Least Common Multiple (LCM) of 31200 and 31217 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31200 and 31217. First we will calculate the prime factors of 31200 and 31217.

Prime Factorization of 31200

Prime factors of 31200 are 2, 3, 5, 13. Prime factorization of 31200 in exponential form is:

31200 = 25 × 31 × 52 × 131

Prime Factorization of 31217

Prime factors of 31217 are 19, 31, 53. Prime factorization of 31217 in exponential form is:

31217 = 191 × 311 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 31200 and 31217.

LCM(31200,31217) = 25 × 31 × 52 × 131 × 191 × 311 × 531
LCM(31200,31217) = 973970400