A mathematical operation that has vast applications in problem-solving is the L.C.M. or Least Common Multiple. What is the L.C.M. ? Well, first let’s understand what a multiple is. A multiple of a number is a number that can be divided by the given number without giving any remainder. Confused?
Let’s take an example. 20 is a multiple of 5 which basically means that 20 can be divided by 5 completely providing a remainder of zero, or basically no remainder. When we talk about the least common multiple or L.C.M., we associate it with a given set of numbers. So, the L.C.M. of a given set of numbers is nothing but the smallest possible number that is completely divisble by all the numbers in the set given to us.
Let’s try to find the L.C.M. of 2 and 5.
Now, 2 has the following multiples:
2*1 = 1
2*2 = 4
2*3 = 6
2*4 = 8
2*5 = 10
Now, the multiples of 5:
5*1 = 5
5*2 = 10
5*3 = 15
5*4 = 20
5*5 = 25
On comparing the multiples of the two numbers we can see that, 10 is a common multiple for 2 and 5 and it is also the smallest multiple that is common to both the numbers. Therefore the L.C.M. of 2 and 5 is 10.
The method we used in this example to determine the L.C.M. is known the multiple method.
Finding the L.C.M. of a given set of numbers has several applications, most importantly in calculations involving fractions. So, let’s get started with our worksheets!
Now, the most basic operation is to determine the L.C.M. of two given numbers and it is important to start with two numbers in order to learn the correct steps. Quick recall of the multiplication table is necessary while solving these problems so don’t be disheartened if you make a few mistakes in the beginning.
Least Common Multiple Worksheets
A great way to get into the habit of mentally determining the multiples is to first practice writing them down. This helps students calculate faster and with time they will be able to calculate it in their head, without having to work it out on paper.
Now, although we have highlighted the multiple methods here, there are two more methods for determining the L.C.M. of a given set of numbers. These are 1. the prime factorization method 2. the common division method.
In the prime factorization method, the prime factors for each of the numbers are determined separately. Then, the common multiples from both the numbers are taken and multiplied to obtain the L.C.M.
In the case of the common division method, the two given numbers are taken as the common dividend and divided by suitable numbers or divisors until they are no longer divisible. Then the quotients and the divisors are multiplied to obtain the L.C.M. of the given numbers.
Practice makes perfect and that phrase is most applicable in mathematics. Errors and mistakes are part of learning and it is important for children to not give up and keep going. Once they get the hang of solving the L.C.M.s of two numbers, they will get better at it and eventually be able to calculate it mentally which will ultimately help them become more efficient at solving problems. Worksheets are a great way for children to approach a new topic in a step by step manner without feeling intimidated by hefty books and never-ending exercises. This helps them learn and understand concepts in a positive way which ultimately helps them learn better.
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