Given Numbers are 69, 74

We can find the LCM of 69, 74 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 69 and 74

Multiples of 69 =69,138,207,276,345,414,483,552,621,690,759,828,897,966,1035,1104,1173,

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 69, 74 which is 5106

So, the LCM of 69, 74 is 5106.

One method for determining the LCM of 69 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 69's prime factorization:

Prime factors of 69 are 3,23.

69 = 3¹×23¹

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: 3,23, 2,37

2¹×3¹×23¹×37¹ = 5106

This shows that the LCM of 69 and 74 is 5106.

The first step in determining the Least Common Multiple of 69 and 74 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 69 and 74:

Lets look at the first ten multiples of these numbers, 69 and 74:

69,138,207,276,345,414,483,552,621,1173 are the first ten multiples of 69.

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 69 and 74, for example, are 828, 1173, and 1184. 5106 is the least common multiple since it is the smallest.

69 and 74 have an LCM of 5106.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69 and 74, than apply into the LCM equation.

GCF(69,74) = 1
LCM(69,74) = ( 69 × 74) / 1
LCM(69,74) = 5106 / 1
LCM(69,74) = 5106

1. What is the LCM of 69 and 74?

The LCM of 69 and 74 is 5106.

2. How to find the lowest common multiple of 69 and 74?

To find the lowest common multiple of 69 and 74, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5106.

3. What are the Factors of 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

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 69 and 74 = 5106

Step 1: Find the prime factorization of 69

69 = 3 x 23

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 = 5106 = 2 x 3 x 23 x 37

Step 4: Therefore, the least common multiple of 69 and 74 is 5106.