What is the Least Common Multiple of 30996 and 31005?

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 30996 and 31005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30996 and 31005, than apply into the LCM equation.

GCF(30996,31005) = 9
LCM(30996,31005) = ( 30996 × 31005) / 9
LCM(30996,31005) = 961030980 / 9
LCM(30996,31005) = 106781220

Least Common Multiple (LCM) of 30996 and 31005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30996 and 31005. First we will calculate the prime factors of 30996 and 31005.

Prime Factorization of 30996

Prime Factorization of 31005

Now multiplying the highest exponent prime factors to calculate the LCM of 30996 and 31005.

LCM(30996,31005) = 2² × 3³ × 7¹ × 41¹ × 5¹ × 13¹ × 53¹
LCM(30996,31005) = 106781220