What is the Least Common Multiple of 14560 and 14565?

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 14560 and 14565 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14560 and 14565, than apply into the LCM equation.

GCF(14560,14565) = 5
LCM(14560,14565) = ( 14560 × 14565) / 5
LCM(14560,14565) = 212066400 / 5
LCM(14560,14565) = 42413280

Least Common Multiple (LCM) of 14560 and 14565 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14560 and 14565. First we will calculate the prime factors of 14560 and 14565.

Prime Factorization of 14560

Prime Factorization of 14565

Now multiplying the highest exponent prime factors to calculate the LCM of 14560 and 14565.

LCM(14560,14565) = 2⁵ × 5¹ × 7¹ × 13¹ × 3¹ × 971¹
LCM(14560,14565) = 42413280