The Least Common Multiple (Lcm) Of 12 And 21

LCM of 12 and 21 How to Find LCM of 12, 21? from www.cuemath.com

Understanding LCM

Before we dive into LCM of 12 and 21, let’s first understand what LCM means. LCM stands for Least Common Multiple, which is the smallest number that both given numbers can divide into without leaving a remainder. In simpler terms, it is the smallest multiple that both numbers have in common.

Calculating LCM

To calculate LCM, we need to find the multiples of both numbers and then identify the smallest one that they have in common. In the case of 12 and 21, we need to list down the multiples of both numbers until we find the smallest one in common. For 12, the multiples are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120… For 21, the multiples are 21, 42, 63, 84, 105, 126, 147, 168, 189, 210… As we can see from the list, the smallest multiple that both 12 and 21 have in common is 84. Therefore, 84 is the LCM of 12 and 21.

Simplifying the Calculation

Listing down multiples can be a tedious task, especially for larger numbers. However, there is a simpler way to calculate LCM using the prime factorization method. First, we need to find the prime factors of both numbers. The prime factors of 12 are 2 x 2 x 3, while the prime factors of 21 are 3 x 7. Next, we need to take the highest power of each prime factor between the two numbers. In this case, 2 x 2 x 3 x 7 gives us 84, which is the LCM of 12 and 21.

The Importance of LCM

LCM may seem like a simple concept, but it has many important applications in real life. For example, it can be used to calculate the time taken for two events to occur simultaneously, or to find the least amount of resources needed to complete a task when multiple factors are involved. In mathematics, LCM is also crucial in simplifying fractions, adding and subtracting fractions with different denominators, and solving equations that involve fractions.

Conclusion

In conclusion, the LCM of 12 and 21 is 84. While calculating LCM may seem like a daunting task at first, it is an important concept that has many practical applications. By understanding how to calculate LCM, we can simplify many mathematical problems and make our lives easier.