What is the Least Common Multiple of 8640 and 8649?

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 8640 and 8649 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8640 and 8649, than apply into the LCM equation.

GCF(8640,8649) = 9
LCM(8640,8649) = ( 8640 × 8649) / 9
LCM(8640,8649) = 74727360 / 9
LCM(8640,8649) = 8303040

Least Common Multiple (LCM) of 8640 and 8649 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8640 and 8649. First we will calculate the prime factors of 8640 and 8649.

Prime Factorization of 8640

Prime Factorization of 8649

Now multiplying the highest exponent prime factors to calculate the LCM of 8640 and 8649.

LCM(8640,8649) = 2⁶ × 3³ × 5¹ × 31²
LCM(8640,8649) = 8303040