What is the Least Common Multiple of 30144 and 30160?

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 30144 and 30160 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30144 and 30160, than apply into the LCM equation.

GCF(30144,30160) = 16
LCM(30144,30160) = ( 30144 × 30160) / 16
LCM(30144,30160) = 909143040 / 16
LCM(30144,30160) = 56821440

Least Common Multiple (LCM) of 30144 and 30160 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30144 and 30160. First we will calculate the prime factors of 30144 and 30160.

Prime Factorization of 30144

Prime Factorization of 30160

Now multiplying the highest exponent prime factors to calculate the LCM of 30144 and 30160.

LCM(30144,30160) = 2⁶ × 3¹ × 157¹ × 5¹ × 13¹ × 29¹
LCM(30144,30160) = 56821440