Given Numbers are 304, 312

We can find the LCM of 304, 312 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 304 and 312

Multiples of 304 =304,608,912,1216,1520,1824,2128,2432,2736,3040,3344,3648,3952,4256,4560,4864,5168,

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 304, 312 which is 11856

So, the LCM of 304, 312 is 11856.

One method for determining the LCM of 304 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 304's prime factorization:

Prime factors of 304 are 2,19.

304 = 2⁴×19¹

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: 2,19, 3,13

2⁴×3¹×13¹×19¹ = 11856

This shows that the LCM of 304 and 312 is 11856.

The first step in determining the Least Common Multiple of 304 and 312 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 304 and 312:

Lets look at the first ten multiples of these numbers, 304 and 312:

304,608,912,1216,1520,1824,2128,2432,2736,5168 are the first ten multiples of 304.

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 304 and 312, for example, are 3648, 5168, and 4992. 11856 is the least common multiple since it is the smallest.

304 and 312 have an LCM of 11856.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 304 and 312, than apply into the LCM equation.

GCF(304,312) = 8
LCM(304,312) = ( 304 × 312) / 8
LCM(304,312) = 94848 / 8
LCM(304,312) = 11856

1. What is the LCM of 304 and 312?

The LCM of 304 and 312 is 11856.

2. How to find the lowest common multiple of 304 and 312?

To find the lowest common multiple of 304 and 312, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11856.

3. What are the Factors of 304?

Answer: Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304. There are 10 integers that are factors of 304. The greatest factor of 304 is 304.

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 304 and 312 = 11856

Step 1: Find the prime factorization of 304

304 = 2 x 2 x 2 x 2 x 19

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 = 11856 = 2 x 2 x 2 x 2 x 3 x 13 x 19

Step 4: Therefore, the least common multiple of 304 and 312 is 11856.