Given Numbers are 126, 130

We can find the LCM of 126, 130 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 126 and 130

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

Multiples of 130 =130,260,390,520,650,780,910,1040,1170,1300,1430,1560,1690,1820,1950,2080,2210,

Now, get the least common multiple of 126, 130 which is 8190

So, the LCM of 126, 130 is 8190.

One method for determining the LCM of 126 and 130 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 130's prime factorization:

Prime factors of 130 are 2, 5,13.

130 = 2¹×5¹×13¹

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, 5,13

2¹×3²×5¹×7¹×13¹ = 8190

This shows that the LCM of 126 and 130 is 8190.

The first step in determining the Least Common Multiple of 126 and 130 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 126 and 130:

Lets look at the first ten multiples of these numbers, 126 and 130:

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

130,260,390,520,650,780,910,1040,1170,2210 are the first ten multiples of 130.

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 130, for example, are 1512, 2142, and 2080. 8190 is the least common multiple since it is the smallest.

126 and 130 have an LCM of 8190.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 126 and 130, than apply into the LCM equation.

GCF(126,130) = 2
LCM(126,130) = ( 126 × 130) / 2
LCM(126,130) = 16380 / 2
LCM(126,130) = 8190

1. What is the LCM of 126 and 130?

The LCM of 126 and 130 is 8190.

2. How to find the lowest common multiple of 126 and 130?

To find the lowest common multiple of 126 and 130, we have to get the multip;es of both numbers and identify the least common multiple in them which is 8190.

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 130?

Answer: Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130. There are 8 integers that are factors of 130. The greatest factor of 130 is 130.

Answer:

Least Common Multiple of 126 and 130 = 8190

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 130

130 = 2 x 5 x 13

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

LCM = 8190 = 2 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 126 and 130 is 8190.