What is the Least Common Multiple of 75996 and 76000?

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 75996 and 76000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75996 and 76000, than apply into the LCM equation.

GCF(75996,76000) = 4
LCM(75996,76000) = ( 75996 × 76000) / 4
LCM(75996,76000) = 5775696000 / 4
LCM(75996,76000) = 1443924000

Least Common Multiple (LCM) of 75996 and 76000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75996 and 76000. First we will calculate the prime factors of 75996 and 76000.

Prime Factorization of 75996

Prime Factorization of 76000

Now multiplying the highest exponent prime factors to calculate the LCM of 75996 and 76000.

LCM(75996,76000) = 2⁵ × 3² × 2111¹ × 5³ × 19¹
LCM(75996,76000) = 1443924000