What is the Least Common Multiple of 40560 and 40575?

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 40560 and 40575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40560 and 40575, than apply into the LCM equation.

GCF(40560,40575) = 15
LCM(40560,40575) = ( 40560 × 40575) / 15
LCM(40560,40575) = 1645722000 / 15
LCM(40560,40575) = 109714800

Least Common Multiple (LCM) of 40560 and 40575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40560 and 40575. First we will calculate the prime factors of 40560 and 40575.

Prime Factorization of 40560

Prime Factorization of 40575

Now multiplying the highest exponent prime factors to calculate the LCM of 40560 and 40575.

LCM(40560,40575) = 2⁴ × 3¹ × 5² × 13² × 541¹
LCM(40560,40575) = 109714800