Given Numbers are 305, 312

We can find the LCM of 305, 312 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 305 and 312

Multiples of 305 =305,610,915,1220,1525,1830,2135,2440,2745,3050,3355,3660,3965,4270,4575,4880,5185,

Multiples of 312 =312,624,936,1248,1560,1872,2184,2496,2808,3120,3432,3744,4056,4368,4680,4992,5304,

Now, get the least common multiple of 305, 312 which is 95160

So, the LCM of 305, 312 is 95160.

One method for determining the LCM of 305 and 312 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 305's prime factorization:

Prime factors of 305 are 5,61.

305 = 5¹×61¹

And this is 312's prime factorization:

Prime factors of 312 are 2, 3,13.

312 = 2³×3¹×13¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 5,61, 2, 3,13

2³×3¹×5¹×13¹×61¹ = 95160

This shows that the LCM of 305 and 312 is 95160.

The first step in determining the Least Common Multiple of 305 and 312 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 305 and 312:

Lets look at the first ten multiples of these numbers, 305 and 312:

305,610,915,1220,1525,1830,2135,2440,2745,5185 are the first ten multiples of 305.

312,624,936,1248,1560,1872,2184,2496,2808,5304 are the first ten multiples of 312.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 305 and 312, for example, are 3660, 5185, and 4992. 95160 is the least common multiple since it is the smallest.

305 and 312 have an LCM of 95160.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 312, than apply into the LCM equation.

GCF(305,312) = 1
LCM(305,312) = ( 305 × 312) / 1
LCM(305,312) = 95160 / 1
LCM(305,312) = 95160

1. What is the LCM of 305 and 312?

The LCM of 305 and 312 is 95160.

2. How to find the lowest common multiple of 305 and 312?

To find the lowest common multiple of 305 and 312, we have to get the multip;es of both numbers and identify the least common multiple in them which is 95160.

3. What are the Factors of 305?

Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.

4. What are the Factors of 312?

Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.

Answer:

Least Common Multiple of 305 and 312 = 95160

Step 1: Find the prime factorization of 305

305 = 5 x 61

Step 2: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 95160 = 2 x 2 x 2 x 3 x 5 x 13 x 61

Step 4: Therefore, the least common multiple of 305 and 312 is 95160.