Given Numbers are 31, 35

We can find the LCM of 31, 35 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 31 and 35

Multiples of 31 =31,62,93,124,155,186,217,248,279,310,341,372,403,434,465,496,527,

Multiples of 35 =35,70,105,140,175,210,245,280,315,350,385,420,455,490,525,560,595,

Now, get the least common multiple of 31, 35 which is 1085

So, the LCM of 31, 35 is 1085.

One method for determining the LCM of 31 and 35 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 31's prime factorization:

Prime factors of 31 are 31.

31 = 31¹

And this is 35's prime factorization:

Prime factors of 35 are 5,7.

35 = 5¹×7¹

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:31, 5,7

5¹×7¹×31¹ = 1085

This shows that the LCM of 31 and 35 is 1085.

The first step in determining the Least Common Multiple of 31 and 35 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 31 and 35:

Lets look at the first ten multiples of these numbers, 31 and 35:

31,62,93,124,155,186,217,248,279,527 are the first ten multiples of 31.

35,70,105,140,175,210,245,280,315,595 are the first ten multiples of 35.

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 31 and 35, for example, are 372, 527, and 560. 1085 is the least common multiple since it is the smallest.

31 and 35 have an LCM of 1085.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 35, than apply into the LCM equation.

GCF(31,35) = 1
LCM(31,35) = ( 31 × 35) / 1
LCM(31,35) = 1085 / 1
LCM(31,35) = 1085

1. What is the LCM of 31 and 35?

The LCM of 31 and 35 is 1085.

2. How to find the lowest common multiple of 31 and 35?

To find the lowest common multiple of 31 and 35, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1085.

3. What are the Factors of 31?

Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.

4. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

Answer:

Least Common Multiple of 31 and 35 = 1085

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 35

35 = 5 x 7

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

LCM = 1085 = 5 x 7 x 31

Step 4: Therefore, the least common multiple of 31 and 35 is 1085.