What is the Least Common Multiple of 31830 and 31850?

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 31830 and 31850 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31830 and 31850, than apply into the LCM equation.

GCF(31830,31850) = 10
LCM(31830,31850) = ( 31830 × 31850) / 10
LCM(31830,31850) = 1013785500 / 10
LCM(31830,31850) = 101378550

Least Common Multiple (LCM) of 31830 and 31850 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31830 and 31850. First we will calculate the prime factors of 31830 and 31850.

Prime Factorization of 31830

Prime Factorization of 31850

Now multiplying the highest exponent prime factors to calculate the LCM of 31830 and 31850.

LCM(31830,31850) = 2¹ × 3¹ × 5² × 1061¹ × 7² × 13¹
LCM(31830,31850) = 101378550