Explaining The Least Common Multiples Of 3 And 4

Write All the Numbers Less Than 100 Which Are Common Multiples of 3 and from www.cuemath.com

Understanding Multiples

Multiples refer to the products obtained when a number is multiplied by another whole number. For instance, the multiples of 3 include 3, 6, 9, 12, and so on. Similarly, the multiples of 4 include 4, 8, 12, 16, and so on.

What is the Least Common Multiple?

The least common multiple is the smallest common multiple between two or more numbers. For instance, the least common multiple of 3 and 4 is the smallest number that is divisible by both 3 and 4.

Method 1: Listing Multiples

To find the least common multiple of 3 and 4, you can list their multiples and then look for the smallest number that appears in both lists. In this case, the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on, while the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on. The smallest number that appears in both lists is 12, so the least common multiple of 3 and 4 is 12.

Method 2: Prime Factorization

Another method of finding the least common multiple is through prime factorization. To use this method, you need to factorize each number into its prime factors. In this case, 3 and 4 can be factorized as follows: 3 = 3 x 1 4 = 2 x 2 Next, you need to write the factors in a way that includes all the prime factors, and then multiply the highest power of each prime factor together. In this case, the prime factors are 2 and 3, and the highest power of each factor is 2 and 1, respectively. Therefore, the least common multiple of 3 and 4 is 2^2 x 3^1, which equals 12.

Application of the Least Common Multiple

The least common multiple is a useful concept in various mathematical operations, such as adding and subtracting fractions. When adding or subtracting fractions with different denominators, you need to find the least common multiple of the denominators and then convert the fractions to equivalent fractions with the same denominator.

Examples

For instance, to add 1/3 and 1/4, you need to find the least common multiple of 3 and 4, which is 12. You then convert the fractions to equivalent fractions with a denominator of 12, which gives you 4/12 and 3/12. Adding these fractions gives you 7/12.

Conclusion

In conclusion, the least common multiple is the smallest number that is divisible by two or more numbers. To find the least common multiple of 3 and 4, you can use either the method of listing multiples or prime factorization. The least common multiple is a useful concept in various mathematical operations, such as adding and subtracting fractions.