What is the Least Common Multiple of 19971 and 19980?

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 19971 and 19980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19971 and 19980, than apply into the LCM equation.

GCF(19971,19980) = 9
LCM(19971,19980) = ( 19971 × 19980) / 9
LCM(19971,19980) = 399020580 / 9
LCM(19971,19980) = 44335620

Least Common Multiple (LCM) of 19971 and 19980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19971 and 19980. First we will calculate the prime factors of 19971 and 19980.

Prime Factorization of 19971

Prime Factorization of 19980

Now multiplying the highest exponent prime factors to calculate the LCM of 19971 and 19980.

LCM(19971,19980) = 3³ × 7¹ × 317¹ × 2² × 5¹ × 37¹
LCM(19971,19980) = 44335620