Given Numbers are 164, 170

We can find the LCM of 164, 170 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 164 and 170

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

Multiples of 170 =170,340,510,680,850,1020,1190,1360,1530,1700,1870,2040,2210,2380,2550,2720,2890,

Now, get the least common multiple of 164, 170 which is 13940

So, the LCM of 164, 170 is 13940.

One method for determining the LCM of 164 and 170 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 170's prime factorization:

Prime factors of 170 are 2, 5,17.

170 = 2¹×5¹×17¹

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: 2,41, 5,17

2²×5¹×17¹×41¹ = 13940

This shows that the LCM of 164 and 170 is 13940.

The first step in determining the Least Common Multiple of 164 and 170 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 164 and 170:

Lets look at the first ten multiples of these numbers, 164 and 170:

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

170,340,510,680,850,1020,1190,1360,1530,2890 are the first ten multiples of 170.

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 170, for example, are 1968, 2788, and 2720. 13940 is the least common multiple since it is the smallest.

164 and 170 have an LCM of 13940.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 164 and 170, than apply into the LCM equation.

GCF(164,170) = 2
LCM(164,170) = ( 164 × 170) / 2
LCM(164,170) = 27880 / 2
LCM(164,170) = 13940

1. What is the LCM of 164 and 170?

The LCM of 164 and 170 is 13940.

2. How to find the lowest common multiple of 164 and 170?

To find the lowest common multiple of 164 and 170, we have to get the multip;es of both numbers and identify the least common multiple in them which is 13940.

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 170?

Answer: Factors of 170 are 1, 2, 5, 10, 17, 34, 85, 170. There are 8 integers that are factors of 170. The greatest factor of 170 is 170.

Answer:

Least Common Multiple of 164 and 170 = 13940

Step 1: Find the prime factorization of 164

164 = 2 x 2 x 41

Step 2: Find the prime factorization of 170

170 = 2 x 5 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 = 13940 = 2 x 2 x 5 x 17 x 41

Step 4: Therefore, the least common multiple of 164 and 170 is 13940.