What is the Least Common Multiple of 36096 and 36105?

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 36096 and 36105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36096 and 36105, than apply into the LCM equation.

GCF(36096,36105) = 3
LCM(36096,36105) = ( 36096 × 36105) / 3
LCM(36096,36105) = 1303246080 / 3
LCM(36096,36105) = 434415360

Least Common Multiple (LCM) of 36096 and 36105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36096 and 36105. First we will calculate the prime factors of 36096 and 36105.

Prime Factorization of 36096

Prime Factorization of 36105

Now multiplying the highest exponent prime factors to calculate the LCM of 36096 and 36105.

LCM(36096,36105) = 2⁸ × 3¹ × 47¹ × 5¹ × 29¹ × 83¹
LCM(36096,36105) = 434415360