Given Numbers are 105, 111

We can find the LCM of 105, 111 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 105 and 111

Multiples of 105 =105,210,315,420,525,630,735,840,945,1050,1155,1260,1365,1470,1575,1680,1785,

Multiples of 111 =111,222,333,444,555,666,777,888,999,1110,1221,1332,1443,1554,1665,1776,1887,

Now, get the least common multiple of 105, 111 which is 3885

So, the LCM of 105, 111 is 3885.

One method for determining the LCM of 105 and 111 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 105's prime factorization:

Prime factors of 105 are 3, 5,7.

105 = 3¹×5¹×7¹

And this is 111's prime factorization:

Prime factors of 111 are 3,37.

111 = 3¹×37¹

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: 3, 5,7,37

3¹×5¹×7¹×37¹ = 3885

This shows that the LCM of 105 and 111 is 3885.

The first step in determining the Least Common Multiple of 105 and 111 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 105 and 111:

Lets look at the first ten multiples of these numbers, 105 and 111:

105,210,315,420,525,630,735,840,945,1785 are the first ten multiples of 105.

111,222,333,444,555,666,777,888,999,1887 are the first ten multiples of 111.

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 105 and 111, for example, are 1260, 1785, and 1776. 3885 is the least common multiple since it is the smallest.

105 and 111 have an LCM of 3885.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 111, than apply into the LCM equation.

GCF(105,111) = 3
LCM(105,111) = ( 105 × 111) / 3
LCM(105,111) = 11655 / 3
LCM(105,111) = 3885

1. What is the LCM of 105 and 111?

The LCM of 105 and 111 is 3885.

2. How to find the lowest common multiple of 105 and 111?

To find the lowest common multiple of 105 and 111, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3885.

3. What are the Factors of 105?

Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.

4. What are the Factors of 111?

Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.

Answer:

Least Common Multiple of 105 and 111 = 3885

Step 1: Find the prime factorization of 105

105 = 3 x 5 x 7

Step 2: Find the prime factorization of 111

111 = 3 x 37

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

LCM = 3885 = 3 x 5 x 7 x 37

Step 4: Therefore, the least common multiple of 105 and 111 is 3885.