Given Numbers are 61, 67

We can find the LCM of 61, 67 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 61 and 67

Multiples of 61 =61,122,183,244,305,366,427,488,549,610,671,732,793,854,915,976,1037,

Multiples of 67 =67,134,201,268,335,402,469,536,603,670,737,804,871,938,1005,1072,1139,

Now, get the least common multiple of 61, 67 which is 4087

So, the LCM of 61, 67 is 4087.

One method for determining the LCM of 61 and 67 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 61's prime factorization:

Prime factors of 61 are 61.

61 = 61¹

And this is 67's prime factorization:

Prime factors of 67 are 67.

67 = 67¹

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:61,67

61¹×67¹ = 4087

This shows that the LCM of 61 and 67 is 4087.

The first step in determining the Least Common Multiple of 61 and 67 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 61 and 67:

Lets look at the first ten multiples of these numbers, 61 and 67:

61,122,183,244,305,366,427,488,549,1037 are the first ten multiples of 61.

67,134,201,268,335,402,469,536,603,1139 are the first ten multiples of 67.

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 61 and 67, for example, are 732, 1037, and 1072. 4087 is the least common multiple since it is the smallest.

61 and 67 have an LCM of 4087.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61 and 67, than apply into the LCM equation.

GCF(61,67) = 1
LCM(61,67) = ( 61 × 67) / 1
LCM(61,67) = 4087 / 1
LCM(61,67) = 4087

1. What is the LCM of 61 and 67?

The LCM of 61 and 67 is 4087.

2. How to find the lowest common multiple of 61 and 67?

To find the lowest common multiple of 61 and 67, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4087.

3. What are the Factors of 61?

Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.

4. What are the Factors of 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

Answer:

Least Common Multiple of 61 and 67 = 4087

Step 1: Find the prime factorization of 61

61 = 61

Step 2: Find the prime factorization of 67

67 = 67

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

LCM = 4087 = 61 x 67

Step 4: Therefore, the least common multiple of 61 and 67 is 4087.