What is the Least Common Multiple of 42096 and 42105?

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 42096 and 42105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42096 and 42105, than apply into the LCM equation.

GCF(42096,42105) = 3
LCM(42096,42105) = ( 42096 × 42105) / 3
LCM(42096,42105) = 1772452080 / 3
LCM(42096,42105) = 590817360

Least Common Multiple (LCM) of 42096 and 42105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42096 and 42105. First we will calculate the prime factors of 42096 and 42105.

Prime Factorization of 42096

Prime Factorization of 42105

Now multiplying the highest exponent prime factors to calculate the LCM of 42096 and 42105.

LCM(42096,42105) = 2⁴ × 3¹ × 877¹ × 5¹ × 7¹ × 401¹
LCM(42096,42105) = 590817360