Given Numbers are 29, 34

We can find the LCM of 29, 34 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 29 and 34

Multiples of 29 =29,58,87,116,145,174,203,232,261,290,319,348,377,406,435,464,493,

Multiples of 34 =34,68,102,136,170,204,238,272,306,340,374,408,442,476,510,544,578,

Now, get the least common multiple of 29, 34 which is 986

So, the LCM of 29, 34 is 986.

One method for determining the LCM of 29 and 34 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 29's prime factorization:

Prime factors of 29 are 29.

29 = 29¹

And this is 34's prime factorization:

Prime factors of 34 are 2,17.

34 = 2¹×17¹

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:29, 2,17

2¹×17¹×29¹ = 986

This shows that the LCM of 29 and 34 is 986.

The first step in determining the Least Common Multiple of 29 and 34 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 29 and 34:

Lets look at the first ten multiples of these numbers, 29 and 34:

29,58,87,116,145,174,203,232,261,493 are the first ten multiples of 29.

34,68,102,136,170,204,238,272,306,578 are the first ten multiples of 34.

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 29 and 34, for example, are 348, 493, and 544. 986 is the least common multiple since it is the smallest.

29 and 34 have an LCM of 986.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29 and 34, than apply into the LCM equation.

GCF(29,34) = 1
LCM(29,34) = ( 29 × 34) / 1
LCM(29,34) = 986 / 1
LCM(29,34) = 986

1. What is the LCM of 29 and 34?

The LCM of 29 and 34 is 986.

2. How to find the lowest common multiple of 29 and 34?

To find the lowest common multiple of 29 and 34, we have to get the multip;es of both numbers and identify the least common multiple in them which is 986.

3. What are the Factors of 29?

Answer: Factors of 29 are 1, 29. There are 2 integers that are factors of 29. The greatest factor of 29 is 29.

4. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

Answer:

Least Common Multiple of 29 and 34 = 986

Step 1: Find the prime factorization of 29

29 = 29

Step 2: Find the prime factorization of 34

34 = 2 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 = 986 = 2 x 17 x 29

Step 4: Therefore, the least common multiple of 29 and 34 is 986.