What is the Least Common Multiple of 45760 and 45768?

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 45760 and 45768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45760 and 45768, than apply into the LCM equation.

GCF(45760,45768) = 8
LCM(45760,45768) = ( 45760 × 45768) / 8
LCM(45760,45768) = 2094343680 / 8
LCM(45760,45768) = 261792960

Least Common Multiple (LCM) of 45760 and 45768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45760 and 45768. First we will calculate the prime factors of 45760 and 45768.

Prime Factorization of 45760

Prime Factorization of 45768

Now multiplying the highest exponent prime factors to calculate the LCM of 45760 and 45768.

LCM(45760,45768) = 2⁶ × 5¹ × 11¹ × 13¹ × 3¹ × 1907¹
LCM(45760,45768) = 261792960