Given Numbers are 305, 310

We can find the LCM of 305, 310 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 305 and 310

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

Multiples of 310 =310,620,930,1240,1550,1860,2170,2480,2790,3100,3410,3720,4030,4340,4650,4960,5270,

Now, get the least common multiple of 305, 310 which is 18910

So, the LCM of 305, 310 is 18910.

One method for determining the LCM of 305 and 310 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 310's prime factorization:

Prime factors of 310 are 2, 5,31.

310 = 2¹×5¹×31¹

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, 2,31

2¹×5¹×31¹×61¹ = 18910

This shows that the LCM of 305 and 310 is 18910.

The first step in determining the Least Common Multiple of 305 and 310 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 305 and 310:

Lets look at the first ten multiples of these numbers, 305 and 310:

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

310,620,930,1240,1550,1860,2170,2480,2790,5270 are the first ten multiples of 310.

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 310, for example, are 3660, 5185, and 4960. 18910 is the least common multiple since it is the smallest.

305 and 310 have an LCM of 18910.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 310, than apply into the LCM equation.

GCF(305,310) = 5
LCM(305,310) = ( 305 × 310) / 5
LCM(305,310) = 94550 / 5
LCM(305,310) = 18910

1. What is the LCM of 305 and 310?

The LCM of 305 and 310 is 18910.

2. How to find the lowest common multiple of 305 and 310?

To find the lowest common multiple of 305 and 310, we have to get the multip;es of both numbers and identify the least common multiple in them which is 18910.

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 310?

Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.

Answer:

Least Common Multiple of 305 and 310 = 18910

Step 1: Find the prime factorization of 305

305 = 5 x 61

Step 2: Find the prime factorization of 310

310 = 2 x 5 x 31

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

LCM = 18910 = 2 x 5 x 31 x 61

Step 4: Therefore, the least common multiple of 305 and 310 is 18910.