Given Numbers are 144, 149

We can find the LCM of 144, 149 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 144 and 149

Multiples of 144 =144,288,432,576,720,864,1008,1152,1296,1440,1584,1728,1872,2016,2160,2304,2448,

Multiples of 149 =149,298,447,596,745,894,1043,1192,1341,1490,1639,1788,1937,2086,2235,2384,2533,

Now, get the least common multiple of 144, 149 which is 21456

So, the LCM of 144, 149 is 21456.

One method for determining the LCM of 144 and 149 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 144's prime factorization:

Prime factors of 144 are 2,3.

144 = 2⁴×3²

And this is 149's prime factorization:

Prime factors of 149 are 149.

149 = 149¹

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: 2,3,149

2⁴×3²×149¹ = 21456

This shows that the LCM of 144 and 149 is 21456.

The first step in determining the Least Common Multiple of 144 and 149 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 144 and 149:

Lets look at the first ten multiples of these numbers, 144 and 149:

144,288,432,576,720,864,1008,1152,1296,2448 are the first ten multiples of 144.

149,298,447,596,745,894,1043,1192,1341,2533 are the first ten multiples of 149.

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 144 and 149, for example, are 1728, 2448, and 2384. 21456 is the least common multiple since it is the smallest.

144 and 149 have an LCM of 21456.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 144 and 149, than apply into the LCM equation.

GCF(144,149) = 1
LCM(144,149) = ( 144 × 149) / 1
LCM(144,149) = 21456 / 1
LCM(144,149) = 21456

1. What is the LCM of 144 and 149?

The LCM of 144 and 149 is 21456.

2. How to find the lowest common multiple of 144 and 149?

To find the lowest common multiple of 144 and 149, we have to get the multip;es of both numbers and identify the least common multiple in them which is 21456.

3. What are the Factors of 144?

Answer: Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. There are 15 integers that are factors of 144. The greatest factor of 144 is 144.

4. What are the Factors of 149?

Answer: Factors of 149 are 1, 149. There are 2 integers that are factors of 149. The greatest factor of 149 is 149.

Answer:

Least Common Multiple of 144 and 149 = 21456

Step 1: Find the prime factorization of 144

144 = 2 x 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 149

149 = 149

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

LCM = 21456 = 2 x 2 x 2 x 2 x 3 x 3 x 149

Step 4: Therefore, the least common multiple of 144 and 149 is 21456.