What is the Least Common Multiple of 45744 and 45760?

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 45744 and 45760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45744 and 45760, than apply into the LCM equation.

GCF(45744,45760) = 16
LCM(45744,45760) = ( 45744 × 45760) / 16
LCM(45744,45760) = 2093245440 / 16
LCM(45744,45760) = 130827840

Least Common Multiple (LCM) of 45744 and 45760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45744 and 45760. First we will calculate the prime factors of 45744 and 45760.

Prime Factorization of 45744

Prime Factorization of 45760

Now multiplying the highest exponent prime factors to calculate the LCM of 45744 and 45760.

LCM(45744,45760) = 2⁶ × 3¹ × 953¹ × 5¹ × 11¹ × 13¹
LCM(45744,45760) = 130827840