Given Numbers are 114, 119

We can find the LCM of 114, 119 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 114 and 119

Multiples of 114 =114,228,342,456,570,684,798,912,1026,1140,1254,1368,1482,1596,1710,1824,1938,

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

Now, get the least common multiple of 114, 119 which is 13566

So, the LCM of 114, 119 is 13566.

One method for determining the LCM of 114 and 119 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 114's prime factorization:

Prime factors of 114 are 2, 3,19.

114 = 2¹×3¹×19¹

And this is 119's prime factorization:

Prime factors of 119 are 7,17.

119 = 7¹×17¹

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, 3,19, 7,17

2¹×3¹×7¹×17¹×19¹ = 13566

This shows that the LCM of 114 and 119 is 13566.

The first step in determining the Least Common Multiple of 114 and 119 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 114 and 119:

Lets look at the first ten multiples of these numbers, 114 and 119:

114,228,342,456,570,684,798,912,1026,1938 are the first ten multiples of 114.

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

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 114 and 119, for example, are 1368, 1938, and 1904. 13566 is the least common multiple since it is the smallest.

114 and 119 have an LCM of 13566.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 114 and 119, than apply into the LCM equation.

GCF(114,119) = 1
LCM(114,119) = ( 114 × 119) / 1
LCM(114,119) = 13566 / 1
LCM(114,119) = 13566

1. What is the LCM of 114 and 119?

The LCM of 114 and 119 is 13566.

2. How to find the lowest common multiple of 114 and 119?

To find the lowest common multiple of 114 and 119, we have to get the multip;es of both numbers and identify the least common multiple in them which is 13566.

3. What are the Factors of 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

4. 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.

Answer:

Least Common Multiple of 114 and 119 = 13566

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

Step 2: Find the prime factorization of 119

119 = 7 x 17

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

LCM = 13566 = 2 x 3 x 7 x 17 x 19

Step 4: Therefore, the least common multiple of 114 and 119 is 13566.