What are multiples? Where do we use them?
There are many reasons which make math a hard and most hated subject by the kids. One of the most important reasons is the insufficient knowledge of basic math concepts such as least common multiple or (lcm) and greatest common factor (gcf). Many students don’t care about these basic concepts when there is a right time to learn these basic concepts.
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In grade three or four students start to learn multiples. Once students start learning multiplication and get comfortable with it, they should learn about multiples.
Multiples are other form of times and actually the word “times” can be interchanged with the word “multiples”. It is the further use of multiples which makes little difference between times (multiplication) and multiples.
If students know the skip counting by two’s then they know the "two times table" and hence they know the multiples of two.
As skip counting by 2’s, if starting at “2” can be written as: 2, 4, 6, 8, 10, 12, 14, 16,…….and so on.
The above pattern is two times table too. Therefore multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 and so on.
Similarly the multiples of other numbers can be written as shown below: (first five multiples only)
3 = 3, 6, 9, 12, 15
4 = 4, 8, 12, 16, 20
5 = 5, 10, 15, 20, 25
6 = 6, 12, 18, 24, 30
7 = 7, 14, 21, 28, 35
12 = 12, 24, 36, 48, 60
13 = 13, 26, 39, 52, 65
From the above examples, it is very clear that multiples are times.
Next thing is to know where the multiples are used?
Knowledge of multiples enhances the basic math skill of times and makes students able to predict multiplication of two numbers right away without any delay. The most important use of multiples is to find least common multiple (lcm), without which fractions can’t be learned and without fractions math is incomplete.
If students know multiples of two or more numbers, then they can find the least common multiple of these numbers easily and which is the only tool to add or subtract fractions with unlike denominators.
Finally, it can be said that the "multiples" are the "times" and to know multiples, students should be very good at times tables up to twenty. Multiples is a must know skill for grade five students. If a grade five student doesn’t know the times tables and hence the multiples, it is hard for this student to get good grades in grade five or higher grades' math. Students should be aware about the usefulness of multiples in finding the least common multiple of two or more numbers and in multiplying two numbers.
Least Common Multiple (LCM):
To find least common multiple or lcm of two numbers, students have to find multiples of both numbers and pick a common multiple which is the smallest of all. That smallest common multiple of both numbers is called the least common multiple.
For example; consider we want to find “lcm” of numbers “6” and “8”. To find “lcm” of these number write the first 5 multiples of both the numbers as shown below:
6 = 6, 12, 18, 24, 30
8 = 8, 16, 24, 32, 40
Now by looking at first five multiples of both the numbers, we can locate the common multiple for both, which is “24”. There is no other multiple smaller than 24 which is common for both the given numbers.
Hence, “24” is the “lcm” of “6” and “8”
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Sometimes there is no common multiple in first five multiples of both the numbers, in this case write the next five multiples to locate the least common multiple.