Given Numbers are 68, 74

We can find the LCM of 68, 74 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 68 and 74

Multiples of 68 =68,136,204,272,340,408,476,544,612,680,748,816,884,952,1020,1088,1156,

Multiples of 74 =74,148,222,296,370,444,518,592,666,740,814,888,962,1036,1110,1184,1258,

Now, get the least common multiple of 68, 74 which is 2516

So, the LCM of 68, 74 is 2516.

One method for determining the LCM of 68 and 74 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 68's prime factorization:

Prime factors of 68 are 2,17.

68 = 2²×17¹

And this is 74's prime factorization:

Prime factors of 74 are 2,37.

74 = 2¹×37¹

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: 2,17,37

2²×17¹×37¹ = 2516

This shows that the LCM of 68 and 74 is 2516.

The first step in determining the Least Common Multiple of 68 and 74 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 68 and 74:

Lets look at the first ten multiples of these numbers, 68 and 74:

68,136,204,272,340,408,476,544,612,1156 are the first ten multiples of 68.

74,148,222,296,370,444,518,592,666,1258 are the first ten multiples of 74.

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 68 and 74, for example, are 816, 1156, and 1184. 2516 is the least common multiple since it is the smallest.

68 and 74 have an LCM of 2516.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68 and 74, than apply into the LCM equation.

GCF(68,74) = 2
LCM(68,74) = ( 68 × 74) / 2
LCM(68,74) = 5032 / 2
LCM(68,74) = 2516

1. What is the LCM of 68 and 74?

The LCM of 68 and 74 is 2516.

2. How to find the lowest common multiple of 68 and 74?

To find the lowest common multiple of 68 and 74, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2516.

3. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. What are the Factors of 74?

Answer: Factors of 74 are 1, 2, 37, 74. There are 4 integers that are factors of 74. The greatest factor of 74 is 74.

Answer:

Least Common Multiple of 68 and 74 = 2516

Step 1: Find the prime factorization of 68

68 = 2 x 2 x 17

Step 2: Find the prime factorization of 74

74 = 2 x 37

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

LCM = 2516 = 2 x 2 x 17 x 37

Step 4: Therefore, the least common multiple of 68 and 74 is 2516.