What is the Least Common Multiple of 19965 and 19971?

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 19965 and 19971 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19965 and 19971, than apply into the LCM equation.

GCF(19965,19971) = 3
LCM(19965,19971) = ( 19965 × 19971) / 3
LCM(19965,19971) = 398721015 / 3
LCM(19965,19971) = 132907005

Least Common Multiple (LCM) of 19965 and 19971 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19965 and 19971. First we will calculate the prime factors of 19965 and 19971.

Prime Factorization of 19965

Prime Factorization of 19971

Now multiplying the highest exponent prime factors to calculate the LCM of 19965 and 19971.

LCM(19965,19971) = 3² × 5¹ × 11³ × 7¹ × 317¹
LCM(19965,19971) = 132907005