Given Numbers are 168, 174

We can find the LCM of 168, 174 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 168 and 174

Multiples of 168 =168,336,504,672,840,1008,1176,1344,1512,1680,1848,2016,2184,2352,2520,2688,2856,

Multiples of 174 =174,348,522,696,870,1044,1218,1392,1566,1740,1914,2088,2262,2436,2610,2784,2958,

Now, get the least common multiple of 168, 174 which is 4872

So, the LCM of 168, 174 is 4872.

One method for determining the LCM of 168 and 174 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 168's prime factorization:

Prime factors of 168 are 2, 3,7.

168 = 2³×3¹×7¹

And this is 174's prime factorization:

Prime factors of 174 are 2, 3,29.

174 = 2¹×3¹×29¹

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, 3,7,29

2³×3¹×7¹×29¹ = 4872

This shows that the LCM of 168 and 174 is 4872.

The first step in determining the Least Common Multiple of 168 and 174 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 168 and 174:

Lets look at the first ten multiples of these numbers, 168 and 174:

168,336,504,672,840,1008,1176,1344,1512,2856 are the first ten multiples of 168.

174,348,522,696,870,1044,1218,1392,1566,2958 are the first ten multiples of 174.

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 168 and 174, for example, are 2016, 2856, and 2784. 4872 is the least common multiple since it is the smallest.

168 and 174 have an LCM of 4872.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 168 and 174, than apply into the LCM equation.

GCF(168,174) = 6
LCM(168,174) = ( 168 × 174) / 6
LCM(168,174) = 29232 / 6
LCM(168,174) = 4872

1. What is the LCM of 168 and 174?

The LCM of 168 and 174 is 4872.

2. How to find the lowest common multiple of 168 and 174?

To find the lowest common multiple of 168 and 174, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4872.

3. What are the Factors of 168?

Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.

4. What are the Factors of 174?

Answer: Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174. There are 8 integers that are factors of 174. The greatest factor of 174 is 174.

Answer:

Least Common Multiple of 168 and 174 = 4872

Step 1: Find the prime factorization of 168

168 = 2 x 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 174

174 = 2 x 3 x 29

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

LCM = 4872 = 2 x 2 x 2 x 3 x 7 x 29

Step 4: Therefore, the least common multiple of 168 and 174 is 4872.