Given Numbers are 174, 178

We can find the LCM of 174, 178 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 174 and 178

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

Multiples of 178 =178,356,534,712,890,1068,1246,1424,1602,1780,1958,2136,2314,2492,2670,2848,3026,

Now, get the least common multiple of 174, 178 which is 15486

So, the LCM of 174, 178 is 15486.

One method for determining the LCM of 174 and 178 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 174's prime factorization:

Prime factors of 174 are 2, 3,29.

174 = 2¹×3¹×29¹

And this is 178's prime factorization:

Prime factors of 178 are 2,89.

178 = 2¹×89¹

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, 3,29,89

2¹×3¹×29¹×89¹ = 15486

This shows that the LCM of 174 and 178 is 15486.

The first step in determining the Least Common Multiple of 174 and 178 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 174 and 178:

Lets look at the first ten multiples of these numbers, 174 and 178:

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

178,356,534,712,890,1068,1246,1424,1602,3026 are the first ten multiples of 178.

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 174 and 178, for example, are 2088, 2958, and 2848. 15486 is the least common multiple since it is the smallest.

174 and 178 have an LCM of 15486.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 174 and 178, than apply into the LCM equation.

GCF(174,178) = 2
LCM(174,178) = ( 174 × 178) / 2
LCM(174,178) = 30972 / 2
LCM(174,178) = 15486

1. What is the LCM of 174 and 178?

The LCM of 174 and 178 is 15486.

2. How to find the lowest common multiple of 174 and 178?

To find the lowest common multiple of 174 and 178, we have to get the multip;es of both numbers and identify the least common multiple in them which is 15486.

3. 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.

4. What are the Factors of 178?

Answer: Factors of 178 are 1, 2, 89, 178. There are 4 integers that are factors of 178. The greatest factor of 178 is 178.

Answer:

Least Common Multiple of 174 and 178 = 15486

Step 1: Find the prime factorization of 174

174 = 2 x 3 x 29

Step 2: Find the prime factorization of 178

178 = 2 x 89

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

LCM = 15486 = 2 x 3 x 29 x 89

Step 4: Therefore, the least common multiple of 174 and 178 is 15486.