Given Numbers are 65, 71

We can find the LCM of 65, 71 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 65 and 71

Multiples of 65 =65,130,195,260,325,390,455,520,585,650,715,780,845,910,975,1040,1105,

Multiples of 71 =71,142,213,284,355,426,497,568,639,710,781,852,923,994,1065,1136,1207,

Now, get the least common multiple of 65, 71 which is 4615

So, the LCM of 65, 71 is 4615.

One method for determining the LCM of 65 and 71 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 65's prime factorization:

Prime factors of 65 are 5,13.

65 = 5¹×13¹

And this is 71's prime factorization:

Prime factors of 71 are 71.

71 = 71¹

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: 5,13,71

5¹×13¹×71¹ = 4615

This shows that the LCM of 65 and 71 is 4615.

The first step in determining the Least Common Multiple of 65 and 71 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 65 and 71:

Lets look at the first ten multiples of these numbers, 65 and 71:

65,130,195,260,325,390,455,520,585,1105 are the first ten multiples of 65.

71,142,213,284,355,426,497,568,639,1207 are the first ten multiples of 71.

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 65 and 71, for example, are 780, 1105, and 1136. 4615 is the least common multiple since it is the smallest.

65 and 71 have an LCM of 4615.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 71, than apply into the LCM equation.

GCF(65,71) = 1
LCM(65,71) = ( 65 × 71) / 1
LCM(65,71) = 4615 / 1
LCM(65,71) = 4615

1. What is the LCM of 65 and 71?

The LCM of 65 and 71 is 4615.

2. How to find the lowest common multiple of 65 and 71?

To find the lowest common multiple of 65 and 71, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4615.

3. What are the Factors of 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

4. What are the Factors of 71?

Answer: Factors of 71 are 1, 71. There are 2 integers that are factors of 71. The greatest factor of 71 is 71.

Answer:

Least Common Multiple of 65 and 71 = 4615

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 71

71 = 71

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

LCM = 4615 = 5 x 13 x 71

Step 4: Therefore, the least common multiple of 65 and 71 is 4615.