What is the Least Common Multiple of 45640 and 45648?

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 45640 and 45648 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45640 and 45648, than apply into the LCM equation.

GCF(45640,45648) = 8
LCM(45640,45648) = ( 45640 × 45648) / 8
LCM(45640,45648) = 2083374720 / 8
LCM(45640,45648) = 260421840

Least Common Multiple (LCM) of 45640 and 45648 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45640 and 45648. First we will calculate the prime factors of 45640 and 45648.

Prime Factorization of 45640

Prime Factorization of 45648

Now multiplying the highest exponent prime factors to calculate the LCM of 45640 and 45648.

LCM(45640,45648) = 2⁴ × 5¹ × 7¹ × 163¹ × 3² × 317¹
LCM(45640,45648) = 260421840