What is the Least Common Multiple of 48945 and 48960?

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 48945 and 48960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48945 and 48960, than apply into the LCM equation.

GCF(48945,48960) = 15
LCM(48945,48960) = ( 48945 × 48960) / 15
LCM(48945,48960) = 2396347200 / 15
LCM(48945,48960) = 159756480

Least Common Multiple (LCM) of 48945 and 48960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48945 and 48960. First we will calculate the prime factors of 48945 and 48960.

Prime Factorization of 48945

Prime Factorization of 48960

Now multiplying the highest exponent prime factors to calculate the LCM of 48945 and 48960.

LCM(48945,48960) = 3² × 5¹ × 13¹ × 251¹ × 2⁶ × 17¹
LCM(48945,48960) = 159756480