Before we can find the LCM (Least Common Multiple) of 74 and 8, let’s define what it means. The LCM is the smallest positive integer that is a multiple of both numbers. In other words, it is the smallest number that both 74 and 8 divide into evenly. To find the LCM, we start by finding the prime factorization of each number.

The prime factorization of 74 can be found by dividing it by the first prime number greater than one, which is 2. We get 37 as the quotient and since 37 is prime, we know that it is the only prime factor. Therefore, we can write the prime factorization of 74 as 2 x 37.

The prime factorization of 8 can be found using the same method. We divide it by 2 and get 4 as the quotient. Then we divide 4 by 2 again and get 2 as the quotient. Finally, we divide 2 by 2 and get 1 as the quotient. We know that 2 is a prime number, so we can write the prime factorization of 8 as 2 x 2 x 2 or 2³.

Now that we have the prime factorization of each number, we can find the LCM. We start by listing all the prime factors of both numbers, making sure to include any repeated factors only once. This gives us: 2 x 2 x 2 x 37.

Next, we write down the highest power of each prime factor that appears in either prime factorization. In this case, 2 appears as 2³ in the prime factorization of 8, but only as 2¹ in the prime factorization of 74. Therefore, we include the highest power of 2, which is 2³. Similarly, 37 appears only in the prime factorization of 74, so we include it with a power of 1.

Finally, we multiply all the prime factors together with their highest powers. This gives us: LCM(74, 8) = 2³ x 37 = 296.

Therefore, the LCM of 74 and 8 is 296. This means that 296 is the smallest positive integer that both 74 and 8 can divide into evenly.

## How to calculate LCM?

LCM stands for Least Common Multiple. It is the smallest whole number that is a multiple of two or more given numbers. To calculate the LCM of a set of numbers, follow the steps below:

Step 1: Write down the prime factorization of each number.

Prime factorization is the process of breaking down a number into its prime factors. For example, the prime factorization of 24 is, 2 × 2 × 2 × 3.

Step 2: Identify the common factors

Look for the factors that are common to all the numbers. Make sure that you include all the powers of each prime factor. For example, If you are calculating the LCM of 12 and 18, the common factors are 2 × 2 × 3 = 12 and 2 × 3 × 3 = 18.

Step 3: Multiply the common factors

Multiply the common factors of the numbers. The LCM of 12 and 18 is 2 × 2 × 3 × 3 = 36.

Step 4: Check for more numbers

If there are more numbers to be included in the LCM calculation, repeat the same process by identifying the common factors and multiplying them together.

For example, if you want to calculate the LCM of 12, 18 and 24, start by finding the prime factorization of each number:

12 = 2 x 2 x 3

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Then identify the common factors: 2 × 2 × 3 = 12 and 2 × 3 × 3 = 18. Note that 24 has a new factor of 2.

Multiply the common factors together: 2 × 2 × 3 × 3 × 2 = 72.

Therefore, the LCM of 12, 18, and 24 is 72.

To calculate the LCM of a set of numbers, find their prime factorization, identify the common factors, and multiply them together. Repeat the process for any additional numbers.

## What two numbers make 74?

There are multiple combinations of two numbers that make 74. One pair of numbers that make 74 are 40 and 34. Another pair of numbers that add up to 74 are 50 and 24. Additionally, you could also have 60 and 14, or 70 and 4. It is important to note that there are both positive and negative pairs of numbers that add up to 74.

For example, 37 and 37 would be a positive pair, while -20 and -54 would be a negative pair. The possibilities are endless, and it ultimately depends on the context and situation in which the question is being asked.

## What is the quickest way to find LCM?

The quickest way to find LCM is through a method called prime factorization. This involves breaking down each number into its prime factors and then determining the product of these prime factors to determine the LCM.

For example, if we need to find the LCM of 12 and 18:

Step 1: Prime factorization of 12 – 2 x 2 x 3

Step 2: Prime factorization of 18 – 2 x 3 x 3

Step 3: Identify the common prime factors – 2 and 3

Step 4: Multiply the common prime factors with the highest exponent – 2 x 2 x 3 x 3 = 36

Therefore, the LCM of 12 and 18 is 36. This is the quickest and most efficient way of finding the LCM. It requires no guessing or trial and error, and it always guarantees an accurate result. This method can be used for any set of numbers, regardless of their size, and can be done mentally or with the aid of a calculator.

## How do you find the LCM of 24 and 35?

Finding the LCM (Least Common Multiple) of two numbers is a common mathematical problem that arises in various fields, including algebra, geometry, and arithmetic. The LCM of two or more numbers refers to the smallest multiple that is common to all of them. To find the LCM of two numbers, it is important to determine the factors of each number and then determine their common multiple.

To find the LCM of 24 and 35, we need to first find the prime factors of both numbers. The prime factors of 24 are 2, 2, 2, and 3, while the prime factors of 35 are 5 and 7. To find the LCM, we need to identify the prime factors that are common to both numbers and the prime factors that are unique to each number.

In this case, the prime factors that are common to both numbers are 2 and 3.

To find the LCM, we need to take the highest power of each prime factor that is present in either number. In this case, we have 2^3 (highest power in 24) and 5 (present in 35 only). We then multiply these values, giving us 2^3 x 5 = 40, which is the LCM of 24 and 35.

Therefore, the LCM of 24 and 35 is 40. This means that 40 is the smallest multiple that is common to both 24 and 35.