What is the Least Common Multiple of 31815 and 31824?

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 31815 and 31824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31815 and 31824, than apply into the LCM equation.

GCF(31815,31824) = 9
LCM(31815,31824) = ( 31815 × 31824) / 9
LCM(31815,31824) = 1012480560 / 9
LCM(31815,31824) = 112497840

Least Common Multiple (LCM) of 31815 and 31824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31815 and 31824. First we will calculate the prime factors of 31815 and 31824.

Prime Factorization of 31815

Prime Factorization of 31824

Now multiplying the highest exponent prime factors to calculate the LCM of 31815 and 31824.

LCM(31815,31824) = 3² × 5¹ × 7¹ × 101¹ × 2⁴ × 13¹ × 17¹
LCM(31815,31824) = 112497840