Given Numbers are 132, 138

We can find the LCM of 132, 138 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 132 and 138

Multiples of 132 =132,264,396,528,660,792,924,1056,1188,1320,1452,1584,1716,1848,1980,2112,2244,

Multiples of 138 =138,276,414,552,690,828,966,1104,1242,1380,1518,1656,1794,1932,2070,2208,2346,

Now, get the least common multiple of 132, 138 which is 3036

So, the LCM of 132, 138 is 3036.

One method for determining the LCM of 132 and 138 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 132's prime factorization:

Prime factors of 132 are 2, 3,11.

132 = 2²×3¹×11¹

And this is 138's prime factorization:

Prime factors of 138 are 2, 3,23.

138 = 2¹×3¹×23¹

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, 3,11,23

2²×3¹×11¹×23¹ = 3036

This shows that the LCM of 132 and 138 is 3036.

The first step in determining the Least Common Multiple of 132 and 138 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 132 and 138:

Lets look at the first ten multiples of these numbers, 132 and 138:

132,264,396,528,660,792,924,1056,1188,2244 are the first ten multiples of 132.

138,276,414,552,690,828,966,1104,1242,2346 are the first ten multiples of 138.

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 132 and 138, for example, are 1584, 2244, and 2208. 3036 is the least common multiple since it is the smallest.

132 and 138 have an LCM of 3036.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 132 and 138, than apply into the LCM equation.

GCF(132,138) = 6
LCM(132,138) = ( 132 × 138) / 6
LCM(132,138) = 18216 / 6
LCM(132,138) = 3036

1. What is the LCM of 132 and 138?

The LCM of 132 and 138 is 3036.

2. How to find the lowest common multiple of 132 and 138?

To find the lowest common multiple of 132 and 138, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3036.

3. What are the Factors of 132?

Answer: Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. There are 12 integers that are factors of 132. The greatest factor of 132 is 132.

4. What are the Factors of 138?

Answer: Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138. There are 8 integers that are factors of 138. The greatest factor of 138 is 138.

Answer:

Least Common Multiple of 132 and 138 = 3036

Step 1: Find the prime factorization of 132

132 = 2 x 2 x 3 x 11

Step 2: Find the prime factorization of 138

138 = 2 x 3 x 23

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

LCM = 3036 = 2 x 2 x 3 x 11 x 23

Step 4: Therefore, the least common multiple of 132 and 138 is 3036.