What is the Least Common Multiple of 54705 and 54720?

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 54705 and 54720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54705 and 54720, than apply into the LCM equation.

GCF(54705,54720) = 15
LCM(54705,54720) = ( 54705 × 54720) / 15
LCM(54705,54720) = 2993457600 / 15
LCM(54705,54720) = 199563840

Least Common Multiple (LCM) of 54705 and 54720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54705 and 54720. First we will calculate the prime factors of 54705 and 54720.

Prime Factorization of 54705

Prime Factorization of 54720

Now multiplying the highest exponent prime factors to calculate the LCM of 54705 and 54720.

LCM(54705,54720) = 3² × 5¹ × 7¹ × 521¹ × 2⁶ × 19¹
LCM(54705,54720) = 199563840