What is the Least Common Multiple of 83580 and 83584?

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 83580 and 83584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 83580 and 83584, than apply into the LCM equation.

GCF(83580,83584) = 4
LCM(83580,83584) = ( 83580 × 83584) / 4
LCM(83580,83584) = 6985950720 / 4
LCM(83580,83584) = 1746487680

Least Common Multiple (LCM) of 83580 and 83584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 83580 and 83584. First we will calculate the prime factors of 83580 and 83584.

Prime Factorization of 83580

Prime Factorization of 83584

Now multiplying the highest exponent prime factors to calculate the LCM of 83580 and 83584.

LCM(83580,83584) = 2⁷ × 3¹ × 5¹ × 7¹ × 199¹ × 653¹
LCM(83580,83584) = 1746487680