What is the Least Common Multiple of 5964 and 5975?

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 5964 and 5975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5964 and 5975, than apply into the LCM equation.

GCF(5964,5975) = 1
LCM(5964,5975) = ( 5964 × 5975) / 1
LCM(5964,5975) = 35634900 / 1
LCM(5964,5975) = 35634900

Least Common Multiple (LCM) of 5964 and 5975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5964 and 5975. First we will calculate the prime factors of 5964 and 5975.

Prime Factorization of 5964

Prime Factorization of 5975

Now multiplying the highest exponent prime factors to calculate the LCM of 5964 and 5975.

LCM(5964,5975) = 2² × 3¹ × 7¹ × 71¹ × 5² × 239¹
LCM(5964,5975) = 35634900