To find the LCM (Least Common Multiple) of two numbers, we need to find the smallest multiple that is common to both of them. Here, we need to find the LCM of 4 and 5.

To begin with, we list the multiples of each number and look for the smallest multiple that appears in both lists.

For 4, the first few multiples are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …

For 5, the first few multiples are:

5, 10, 15, 20, 25, 30, 35, 40, 45, …

From the above lists, we can see that the smallest multiple that appears in both lists is 20. Therefore, the LCM of 4 and 5 is 20.

We found the LCM of 4 and 5 by listing their multiples and looking for the smallest multiple that appears in both lists. We found that the LCM is 20.

## How to calculate LCM?

LCM or Least Common Multiple is the smallest positive integer that is divisible by two or more numbers. It is a commonly used mathematical technique in many fields and is used to solve several real-life problems. The LCM is used in many mathematical operations, including calculating fractions and simplifying algebraic expressions.

To calculate LCM, we need to follow a systematic approach. We can use different methods to find LCM based on the given numbers. The most commonly used method is the prime factorization method.

The prime factorization method involves the following steps:

1. Write down the prime factorization of each of the given numbers. For example, let us consider two numbers, 12 and 18.

12 = 2 x 2 x 3

18 = 2 x 3 x 3

2. Write down all the prime factors of the given numbers.

2, 2, 3

2, 3, 3

3. Identify the common prime factors, and write them down once.

2, 3

4. Multiply the common factors from step 3. This gives us the LCM of the given numbers.

2 x 3 = 6

Hence, the LCM of 12 and 18 is 6.

Another method to find the LCM is by using the “Division Method.” This involves the following steps:

1. Write down the given numbers.

2. Divide the numbers by the least common multiple of the two numbers. If the result is a whole number, continue to step 3. If not, then repeat step 2 by dividing the larger number by the same divisor.

3. Write down the quotient obtained in the previous step below the numbers and repeat step 2 with the new set of numbers.

4. Continue the steps above until you get the same quotient for all the numbers.

5. Finally, the LCM is obtained by multiplying the common divisors and all the quotients.

Let us consider two numbers, 12 and 18.

Step 1: Write down the given numbers; 12, 18.

Step 2: Divide the larger number by the small number.

18 ÷ 12 = 1 with a remainder of 6.

Step 3: Write down the quotient obtained and the remainder under the larger number. Therefore, the new set of numbers is 12 and 6.

Step 4: Divide the larger number by the remainder obtained in the previous step.

12 ÷ 6= 2.

Step 5: Write down the quotient obtained in step 4 under 6.

Step 6: Since the quotient obtained is 2 for both numbers, we can stop the division process.

Step 7: The LCM is calculated by multiplying the common divisor (2), 12 and 18.

LCM = 2 × 12 × 18

LCM = 432.

Therefore, the LCM of 12 and 18 is 432.

The LCM is an important mathematical concept that has numerous applications in mathematics and science. Different approaches can be used to calculate the LCM, depending on the given numbers. The prime factorization method is the most widely used and can be used to find the LCM of any set of numbers.

The division method is often used to find the LCM of larger sets of numbers.

## What is the quickest way to find LCM?

The quickest way to find the LCM (Least Common Multiple) is by using the prime factorization method. The prime factorization of a number shows its factors which are all prime numbers. To find the LCM of any number, you should first find the prime factors of all the numbers involved in the problem.

For instance, let’s say we need to find the LCM of 24 and 30.

The prime factors of 24 are 2, 2, 2, and 3. The prime factors of 30 are 2, 3, and 5.

Next, identify each factor the numbers have in common. In this case, both of them have 2 and 3 in common.

So, to find the LCM, you simply need to multiply the highest powers of each prime factor. In this case, the highest power of 2 and 3 are 2 and 1 respectively. We also need to include the prime factor 5 as 30 has this factor that 24 does not have.

Therefore, the LCM of 24 and 30 is 2^2 * 3^1 * 5^1 = 120.

The quickest way to find the LCM is by using prime factorization method. It helps to find the greatest common factor (GCF) and the remaining prime factors. Finally, the LCM can be determined by the product of the GCF and the remaining prime factors of the numbers. The prime factorization method works efficiently for small to mid-range numbers, and multiplication methods can be used for larger numbers.

## How do you find the LCD between two fractions?

The LCD or Least Common Denominator is basically a common multiple of the denominators of two given fractions. It is the smallest possible denominator that both fractions can be converted into in order to add, subtract or compare them. It is essential to have a common denominator when adding or subtracting fractions, although it may not always be required when comparing two fractions.

The process of finding the LCD between two fractions involves the following steps:

Step 1: Find the prime factors of each of the denominators.

Step 2: Make a list of all the prime factors that appear in any of the denominators. Each prime factor should be included the maximum number of times it appears in any of the denominators.

Step 3: Multiply all the prime factors from the list obtained in step 2.

Step 4: The product obtained in step 3 would be the LCD of the two given fractions.

Let us take an example to understand this process better. Consider two fractions, 2/5 and 1/2.

Step 1: Factors of 5 are 5 and 1. Factors of 2 are 2 and 1.

Step 2: The prime factors that appear in the denominators are 2, 5 and 1.

Step 3: Multiply all prime factors, 2 × 5 × 1 = 10.

Step 4: Therefore 10 is the LCD of the fractions 2/5 and 1/2.

In some cases, fractions may have the same denominator, in which case the LCD would simply be the denominators. However, when dealing with large and complex fractions, finding the LCD becomes essential in order to simplify calculations and obtain accurate solutions.

Finding the LCD between two fractions requires the identification of all the prime factors present in the denominators of the given fractions and then making a list of them. The LCD is then obtained by multiplying all the prime factors appearing in the list. The LCD is very beneficial for adding and subtracting fractions, which require a common denominator.

## How to find the LCM on a calculator?

To find the LCM (Least Common Multiple) on a calculator, there are a few steps that you can follow.

Step 1: Enter the numbers

Firstly, enter the two numbers or a series of numbers whose LCM you want to find.

Step 2: Find the prime factorization

The next step is to find the prime factorization of each number. To do this, divide each number by its prime factors until you end up with a set of prime factors. For instance, if you have the number 12, you would divide it by 2, leaving you with 6, which can then be divided by 2 again to give you 3.

Thus, the prime factorization of 12 is 2 x 2 x 3.

Step 3: Find the highest powers of the prime factors

Once you have found the prime factorizations of both numbers, find the highest powers of the prime factors. In other words, write down all the prime factors of both numbers and compare them. Pick the highest power of each prime factor that appears in either number. For example, if you have the numbers 12 and 24, the prime factorization of 12 is 2 x 2 x 3, while that of 24 is 2 x 2 x 2 x 3.

To find the LCM of these two numbers, you would pick the highest power of each prime factor, which would be 2 x 2 x 2 x 3.

Step 4: Multiply the highest powers

The final step in finding the LCM is to multiply the highest powers of the prime factors that you identified in the previous step. Continuing with the example above, 2 x 2 x 2 x 3 equals 24, thus the LCM of 12 and 24 is 24.

All the above steps can be performed on a calculator, and there are even some calculators that have a direct LCM function. Therefore, by following these steps or by using the LCM function on a calculator, you can easily find the LCM of any two numbers.