Explaining The Least Common Multiple Of 2 And 6

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What is a Multiple?

A multiple is a number that can be divided by another number without leaving a remainder. For example, the multiples of 2 are 2, 4, 6, 8, 10, and so on.

What is the Least Common Multiple (LCM)?

The Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 2 and 6 is 6, because 6 is the smallest number that is a multiple of both 2 and 6.

How to Find the LCM of 2 and 6?

There are different methods to find the LCM of two numbers, but one common method is to list their multiples and find the smallest multiple they have in common. Let's do this for 2 and 6: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60... From this list, we can see that the smallest multiple that 2 and 6 have in common is 6. Therefore, the LCM of 2 and 6 is 6.

Why is the LCM Useful?

The LCM is useful in many mathematical operations, such as adding and subtracting fractions with different denominators. In order to add or subtract fractions, their denominators must be the same. The LCM helps us find the least common denominator for two or more fractions.

Examples of Using the LCM

Let's say we want to add the fractions 1/2 and 2/6. The denominators are different, so we need to find the least common denominator. We can use the LCM of 2 and 6, which is 6. To convert 1/2 to an equivalent fraction with denominator 6, we multiply both the numerator and denominator by 3: 1/2 = 3/6 To convert 2/6 to an equivalent fraction with denominator 6, we multiply both the numerator and denominator by 2: 2/6 = 2/6 x 2/2 = 4/6 Now we can add the two fractions: 1/2 + 2/6 = 3/6 + 4/6 = 7/6 However, 7/6 is an improper fraction (the numerator is greater than the denominator). We can simplify it by dividing both the numerator and denominator by their greatest common factor (GCF), which is 1: 7/6 = 1 1/6 Therefore, 1/2 + 2/6 = 1 1/6.

Conclusion

The LCM is the smallest multiple that is common to two or more numbers. In order to find the LCM of two numbers, we can list their multiples and find the smallest multiple they have in common. The LCM is useful in many mathematical operations, such as adding and subtracting fractions with different denominators. By using the LCM, we can find the least common denominator for two or more fractions and convert them to equivalent fractions with the same denominator.