Given Numbers are 312, 320

We can find the LCM of 312, 320 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 312 and 320

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

Multiples of 320 =320,640,960,1280,1600,1920,2240,2560,2880,3200,3520,3840,4160,4480,4800,5120,5440,

Now, get the least common multiple of 312, 320 which is 12480

So, the LCM of 312, 320 is 12480.

One method for determining the LCM of 312 and 320 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 312's prime factorization:

Prime factors of 312 are 2, 3,13.

312 = 2³×3¹×13¹

And this is 320's prime factorization:

Prime factors of 320 are 2,5.

320 = 2⁶×5¹

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, 3,13,5

2⁶×3¹×5¹×13¹ = 12480

This shows that the LCM of 312 and 320 is 12480.

The first step in determining the Least Common Multiple of 312 and 320 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 312 and 320:

Lets look at the first ten multiples of these numbers, 312 and 320:

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

320,640,960,1280,1600,1920,2240,2560,2880,5440 are the first ten multiples of 320.

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 312 and 320, for example, are 3744, 5304, and 5120. 12480 is the least common multiple since it is the smallest.

312 and 320 have an LCM of 12480.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 320, than apply into the LCM equation.

GCF(312,320) = 8
LCM(312,320) = ( 312 × 320) / 8
LCM(312,320) = 99840 / 8
LCM(312,320) = 12480

1. What is the LCM of 312 and 320?

The LCM of 312 and 320 is 12480.

2. How to find the lowest common multiple of 312 and 320?

To find the lowest common multiple of 312 and 320, we have to get the multip;es of both numbers and identify the least common multiple in them which is 12480.

3. 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.

4. What are the Factors of 320?

Answer: Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. There are 14 integers that are factors of 320. The greatest factor of 320 is 320.

Answer:

Least Common Multiple of 312 and 320 = 12480

Step 1: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

Step 2: Find the prime factorization of 320

320 = 2 x 2 x 2 x 2 x 2 x 2 x 5

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

LCM = 12480 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 312 and 320 is 12480.