What is the Least Common Multiple of 45600 and 45605?

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 45600 and 45605 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45600 and 45605, than apply into the LCM equation.

GCF(45600,45605) = 5
LCM(45600,45605) = ( 45600 × 45605) / 5
LCM(45600,45605) = 2079588000 / 5
LCM(45600,45605) = 415917600

Least Common Multiple (LCM) of 45600 and 45605 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45600 and 45605. First we will calculate the prime factors of 45600 and 45605.

Prime Factorization of 45600

Prime Factorization of 45605

Now multiplying the highest exponent prime factors to calculate the LCM of 45600 and 45605.

LCM(45600,45605) = 2⁵ × 3¹ × 5² × 19¹ × 7¹ × 1303¹
LCM(45600,45605) = 415917600