What is the Least Common Multiple of 31905 and 31920?

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 31905 and 31920 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31905 and 31920, than apply into the LCM equation.

GCF(31905,31920) = 15
LCM(31905,31920) = ( 31905 × 31920) / 15
LCM(31905,31920) = 1018407600 / 15
LCM(31905,31920) = 67893840

Least Common Multiple (LCM) of 31905 and 31920 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31905 and 31920. First we will calculate the prime factors of 31905 and 31920.

Prime Factorization of 31905

Prime Factorization of 31920

Now multiplying the highest exponent prime factors to calculate the LCM of 31905 and 31920.

LCM(31905,31920) = 3² × 5¹ × 709¹ × 2⁴ × 7¹ × 19¹
LCM(31905,31920) = 67893840