What is the Least Common Multiple of 19824 and 19839?

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 19824 and 19839 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19824 and 19839, than apply into the LCM equation.

GCF(19824,19839) = 3
LCM(19824,19839) = ( 19824 × 19839) / 3
LCM(19824,19839) = 393288336 / 3
LCM(19824,19839) = 131096112

Least Common Multiple (LCM) of 19824 and 19839 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19824 and 19839. First we will calculate the prime factors of 19824 and 19839.

Prime Factorization of 19824

Prime Factorization of 19839

Now multiplying the highest exponent prime factors to calculate the LCM of 19824 and 19839.

LCM(19824,19839) = 2⁴ × 3¹ × 7¹ × 59¹ × 17¹ × 389¹
LCM(19824,19839) = 131096112