The Lcm Of 12 And 4: Explanation And Solution

LCM of 4 and 12 How to Find LCM of 4, 12? from www.cuemath.com

Understanding LCM

LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more given numbers. In other words, it is the smallest number that both 12 and 4 can divide into evenly without leaving a remainder. Finding the LCM of two or more numbers is useful in many areas of mathematics, including fractions, ratios, and algebra.

Factors of 12 and 4

To find the LCM of 12 and 4, we first need to list their factors. Factors are the numbers that can be multiplied together to get the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 4 are 1, 2, and 4.

Finding the Common Factors

Next, we need to find the factors that are common to both 12 and 4. These are the numbers that both 12 and 4 can be divided by without leaving a remainder. In this case, the common factors are 1 and 2.

Multiplying the Common Factors

To find the LCM, we simply need to multiply the common factors together. In this case, 1 x 2 = 2. Therefore, the LCM of 12 and 4 is 2.

Checking the Answer

To check our answer, we can divide the LCM by each of the original numbers and make sure there is no remainder. In this case, 2 divided by 12 is 0 with a remainder of 2, and 2 divided by 4 is 0 with no remainder. Therefore, 2 is indeed the LCM of 12 and 4.

Using Prime Factorization

Another method for finding the LCM is through prime factorization. Prime factorization is breaking down a number into its prime factors, which are the numbers that can only be divided by 1 and themselves. For example, the prime factors of 12 are 2 x 2 x 3, while the prime factors of 4 are 2 x 2.

Multiplying the Prime Factors

To find the LCM using prime factorization, we need to list the prime factors of each number and then multiply them together. However, we only need to include each prime factor once, and we need to include any factors that are not common to both numbers. In this case, the prime factors of 12 are 2 x 2 x 3, while the prime factors of 4 are 2 x 2. We need to include the 2, the 2, and the 3, since they are all prime factors of 12. Therefore, the LCM is 2 x 2 x 3 = 12.

Choosing a Method

Both methods for finding the LCM are valid and will give the same answer. The method you choose may depend on personal preference or the numbers involved. Prime factorization may be more useful for larger numbers, while listing factors may be easier for smaller numbers.

Conclusion

In conclusion, the LCM of 12 and 4 is 2. This can be found by listing the factors of 12 and 4, finding the common factors, and multiplying them together. Alternatively, it can be found by listing the prime factors of 12 and 4, including each factor once, and multiplying them together. Both methods will give the same answer and can be used depending on personal preference or the numbers involved.