What is the Least Common Multiple of 30984 and 30996?

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 30984 and 30996 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30984 and 30996, than apply into the LCM equation.

GCF(30984,30996) = 12
LCM(30984,30996) = ( 30984 × 30996) / 12
LCM(30984,30996) = 960380064 / 12
LCM(30984,30996) = 80031672

Least Common Multiple (LCM) of 30984 and 30996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30984 and 30996. First we will calculate the prime factors of 30984 and 30996.

Prime Factorization of 30984

Prime Factorization of 30996

Now multiplying the highest exponent prime factors to calculate the LCM of 30984 and 30996.

LCM(30984,30996) = 2³ × 3³ × 1291¹ × 7¹ × 41¹
LCM(30984,30996) = 80031672