What is the Least Common Multiple of 31854 and 31860?

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 31854 and 31860 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31854 and 31860, than apply into the LCM equation.

GCF(31854,31860) = 6
LCM(31854,31860) = ( 31854 × 31860) / 6
LCM(31854,31860) = 1014868440 / 6
LCM(31854,31860) = 169144740

Least Common Multiple (LCM) of 31854 and 31860 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31854 and 31860. First we will calculate the prime factors of 31854 and 31860.

Prime Factorization of 31854

Prime Factorization of 31860

Now multiplying the highest exponent prime factors to calculate the LCM of 31854 and 31860.

LCM(31854,31860) = 2² × 3³ × 5309¹ × 5¹ × 59¹
LCM(31854,31860) = 169144740