What is the Least Common Multiple of 30975 and 30984?

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 30975 and 30984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30975 and 30984, than apply into the LCM equation.

GCF(30975,30984) = 3
LCM(30975,30984) = ( 30975 × 30984) / 3
LCM(30975,30984) = 959729400 / 3
LCM(30975,30984) = 319909800

Least Common Multiple (LCM) of 30975 and 30984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30975 and 30984. First we will calculate the prime factors of 30975 and 30984.

Prime Factorization of 30975

Prime Factorization of 30984

Now multiplying the highest exponent prime factors to calculate the LCM of 30975 and 30984.

LCM(30975,30984) = 3¹ × 5² × 7¹ × 59¹ × 2³ × 1291¹
LCM(30975,30984) = 319909800