Given Numbers are 164, 169

We can find the LCM of 164, 169 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 164 and 169

Multiples of 164 =164,328,492,656,820,984,1148,1312,1476,1640,1804,1968,2132,2296,2460,2624,2788,

Multiples of 169 =169,338,507,676,845,1014,1183,1352,1521,1690,1859,2028,2197,2366,2535,2704,2873,

Now, get the least common multiple of 164, 169 which is 27716

So, the LCM of 164, 169 is 27716.

One method for determining the LCM of 164 and 169 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 164's prime factorization:

Prime factors of 164 are 2,41.

164 = 2²×41¹

And this is 169's prime factorization:

Prime factors of 169 are 13.

169 = 13²

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: 2,41,13

2²×13²×41¹ = 27716

This shows that the LCM of 164 and 169 is 27716.

The first step in determining the Least Common Multiple of 164 and 169 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 164 and 169:

Lets look at the first ten multiples of these numbers, 164 and 169:

164,328,492,656,820,984,1148,1312,1476,2788 are the first ten multiples of 164.

169,338,507,676,845,1014,1183,1352,1521,2873 are the first ten multiples of 169.

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 164 and 169, for example, are 1968, 2788, and 2704. 27716 is the least common multiple since it is the smallest.

164 and 169 have an LCM of 27716.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 164 and 169, than apply into the LCM equation.

GCF(164,169) = 1
LCM(164,169) = ( 164 × 169) / 1
LCM(164,169) = 27716 / 1
LCM(164,169) = 27716

1. What is the LCM of 164 and 169?

The LCM of 164 and 169 is 27716.

2. How to find the lowest common multiple of 164 and 169?

To find the lowest common multiple of 164 and 169, we have to get the multip;es of both numbers and identify the least common multiple in them which is 27716.

3. What are the Factors of 164?

Answer: Factors of 164 are 1, 2, 4, 41, 82, 164. There are 6 integers that are factors of 164. The greatest factor of 164 is 164.

4. What are the Factors of 169?

Answer: Factors of 169 are 1, 13, 169. There are 3 integers that are factors of 169. The greatest factor of 169 is 169.

Answer:

Least Common Multiple of 164 and 169 = 27716

Step 1: Find the prime factorization of 164

164 = 2 x 2 x 41

Step 2: Find the prime factorization of 169

169 = 13 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 = 27716 = 2 x 2 x 13 x 13 x 41

Step 4: Therefore, the least common multiple of 164 and 169 is 27716.