What is the Least Common Multiple of 5965 and 5985?

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 5965 and 5985 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5965 and 5985, than apply into the LCM equation.

GCF(5965,5985) = 5
LCM(5965,5985) = ( 5965 × 5985) / 5
LCM(5965,5985) = 35700525 / 5
LCM(5965,5985) = 7140105

Least Common Multiple (LCM) of 5965 and 5985 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5965 and 5985. First we will calculate the prime factors of 5965 and 5985.

Prime Factorization of 5965

Prime Factorization of 5985

Now multiplying the highest exponent prime factors to calculate the LCM of 5965 and 5985.

LCM(5965,5985) = 5¹ × 1193¹ × 3² × 7¹ × 19¹
LCM(5965,5985) = 7140105