Given Numbers are 119, 126

We can find the LCM of 119, 126 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 119 and 126

Multiples of 119 =119,238,357,476,595,714,833,952,1071,1190,1309,1428,1547,1666,1785,1904,2023,

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

Now, get the least common multiple of 119, 126 which is 2142

So, the LCM of 119, 126 is 2142.

One method for determining the LCM of 119 and 126 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 119's prime factorization:

Prime factors of 119 are 7,17.

119 = 7¹×17¹

And this is 126's prime factorization:

Prime factors of 126 are 2, 3,7.

126 = 2¹×3²×7¹

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: 7,17, 2,3

2¹×3²×7¹×17¹ = 2142

This shows that the LCM of 119 and 126 is 2142.

The first step in determining the Least Common Multiple of 119 and 126 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 119 and 126:

Lets look at the first ten multiples of these numbers, 119 and 126:

119,238,357,476,595,714,833,952,1071,2023 are the first ten multiples of 119.

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

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 119 and 126, for example, are 1428, 2023, and 2016. 2142 is the least common multiple since it is the smallest.

119 and 126 have an LCM of 2142.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 119 and 126, than apply into the LCM equation.

GCF(119,126) = 7
LCM(119,126) = ( 119 × 126) / 7
LCM(119,126) = 14994 / 7
LCM(119,126) = 2142

1. What is the LCM of 119 and 126?

The LCM of 119 and 126 is 2142.

2. How to find the lowest common multiple of 119 and 126?

To find the lowest common multiple of 119 and 126, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2142.

3. What are the Factors of 119?

Answer: Factors of 119 are 1, 7, 17, 119. There are 4 integers that are factors of 119. The greatest factor of 119 is 119.

4. 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.

Answer:

Least Common Multiple of 119 and 126 = 2142

Step 1: Find the prime factorization of 119

119 = 7 x 17

Step 2: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

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

LCM = 2142 = 2 x 3 x 3 x 7 x 17

Step 4: Therefore, the least common multiple of 119 and 126 is 2142.