What is the Least Common Multiple of 5976 and 5984?

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 5976 and 5984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5976 and 5984, than apply into the LCM equation.

GCF(5976,5984) = 8
LCM(5976,5984) = ( 5976 × 5984) / 8
LCM(5976,5984) = 35760384 / 8
LCM(5976,5984) = 4470048

Least Common Multiple (LCM) of 5976 and 5984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5976 and 5984. First we will calculate the prime factors of 5976 and 5984.

Prime Factorization of 5976

Prime Factorization of 5984

Now multiplying the highest exponent prime factors to calculate the LCM of 5976 and 5984.

LCM(5976,5984) = 2⁵ × 3² × 83¹ × 11¹ × 17¹
LCM(5976,5984) = 4470048