Explaining Lcm Of 12 And 28

First Three Common Multiples of 12 and 28 LucahasBoyer from luca-has-boyer.blogspot.com

Understanding LCM

LCM stands for Least Common Multiple. It is the smallest multiple that is common to two or more numbers. In simpler terms, it is the smallest number that is divisible by both the given numbers without leaving any remainder. LCM is a fundamental concept in mathematics and is used in various applications such as simplifying fractions, adding and subtracting fractions, and finding equivalent fractions.

Finding the Factors

To find the LCM of 12 and 28, we first need to find the factors of both numbers. Factors are the numbers that can divide the given number without leaving any remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 28 are 1, 2, 4, 7, 14, and 28.

Identifying Common Factors

Now that we know the factors of both numbers, we need to identify the common factors. Common factors are the factors that both numbers share. The common factors of 12 and 28 are 1, 2, and 4.

Multiplying Common Factors

To find the LCM, we need to multiply the common factors. In this case, the common factors are 1, 2, and 4. Multiplying them together gives us 8. Therefore, the LCM of 12 and 28 is 8.

Checking the Answer

We can check our answer by dividing the LCM by each number and verifying that there is no remainder. When we divide 8 by 12, we get 0.6667, which is not a whole number. When we divide 8 by 28, we get 0.2857, which is also not a whole number. Therefore, our answer is correct.

LCM in Real Life

LCM is a useful concept in real life. For example, if you want to plan a camping trip and need to know when you can all meet up, you can use LCM. Let's say that one person is free every 3 days and another person is free every 4 days. To find the next time they can both meet up, you can use LCM. The LCM of 3 and 4 is 12, so they can meet up every 12 days.

Tricks to Find LCM

There are some tricks to find LCM. One of them is the Prime Factorization Method. In this method, we first find out the prime factors of both numbers and then multiply them together. For example, the prime factors of 12 are 2, 2, and 3. The prime factors of 28 are 2, 2, 7. Multiplying them together gives us 2 x 2 x 3 x 7 = 84, which is the LCM of 12 and 28.

Conclusion

In conclusion, LCM is an important concept in mathematics that is used in various applications. To find the LCM of two numbers, we need to find the factors, identify the common factors, and multiply them together. There are different methods to find LCM, such as the Prime Factorization Method. LCM is also useful in real life situations, such as planning a meeting or event.