Given Numbers are 126, 133

We can find the LCM of 126, 133 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 126 and 133

Multiples of 126 =126,252,378,504,630,756,882,1008,1134,1260,1386,1512,1638,1764,1890,2016,2142,

Multiples of 133 =133,266,399,532,665,798,931,1064,1197,1330,1463,1596,1729,1862,1995,2128,2261,

Now, get the least common multiple of 126, 133 which is 2394

So, the LCM of 126, 133 is 2394.

One method for determining the LCM of 126 and 133 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 126's prime factorization:

Prime factors of 126 are 2, 3,7.

126 = 2¹×3²×7¹

And this is 133's prime factorization:

Prime factors of 133 are 7,19.

133 = 7¹×19¹

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: 2, 3,7,19

2¹×3²×7¹×19¹ = 2394

This shows that the LCM of 126 and 133 is 2394.

The first step in determining the Least Common Multiple of 126 and 133 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 126 and 133:

Lets look at the first ten multiples of these numbers, 126 and 133:

126,252,378,504,630,756,882,1008,1134,2142 are the first ten multiples of 126.

133,266,399,532,665,798,931,1064,1197,2261 are the first ten multiples of 133.

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 126 and 133, for example, are 1512, 2142, and 2128. 2394 is the least common multiple since it is the smallest.

126 and 133 have an LCM of 2394.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 126 and 133, than apply into the LCM equation.

GCF(126,133) = 7
LCM(126,133) = ( 126 × 133) / 7
LCM(126,133) = 16758 / 7
LCM(126,133) = 2394

1. What is the LCM of 126 and 133?

The LCM of 126 and 133 is 2394.

2. How to find the lowest common multiple of 126 and 133?

To find the lowest common multiple of 126 and 133, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2394.

3. What are the Factors of 126?

Answer: Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. There are 12 integers that are factors of 126. The greatest factor of 126 is 126.

4. What are the Factors of 133?

Answer: Factors of 133 are 1, 7, 19, 133. There are 4 integers that are factors of 133. The greatest factor of 133 is 133.

Answer:

Least Common Multiple of 126 and 133 = 2394

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 133

133 = 7 x 19

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

LCM = 2394 = 2 x 3 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 126 and 133 is 2394.