What is the Least Common Multiple of 58128 and 58140?

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 58128 and 58140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58128 and 58140, than apply into the LCM equation.

GCF(58128,58140) = 12
LCM(58128,58140) = ( 58128 × 58140) / 12
LCM(58128,58140) = 3379561920 / 12
LCM(58128,58140) = 281630160

Least Common Multiple (LCM) of 58128 and 58140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 58128 and 58140. First we will calculate the prime factors of 58128 and 58140.

Prime Factorization of 58128

Prime Factorization of 58140

Now multiplying the highest exponent prime factors to calculate the LCM of 58128 and 58140.

LCM(58128,58140) = 2⁴ × 3² × 7¹ × 173¹ × 5¹ × 17¹ × 19¹
LCM(58128,58140) = 281630160