Lesson1:
Code: LE/02/2019
Topic: Multiple, Common
Multiples and Least Common Multiple
Multiple
1.
Google Search Engine: a number that may be
divided by another a certain number of times without a remainder. "15, 20, or any multiple
of five"
In this lesson you will
learn what multiple of a number is. The idea of multiple came from
multiplication table.
Multiplication Table
Multiplication table is a list of multiples of a
particular number, usually from 1 to 12.When you are learning your
multiplication table you are learning multiples. For instance, when you divide
a number by another number without any remainder that number is a multiple of
the number you divided with i.e. the multiples of 7 are 7, 14, 21, 28, 35, 42,
49, 56, etc, if you divide 28 by 7 the result is 4 remainder nothing. In that
case, 28 is a multiple of 7.
If you are asked to list
first ten (10) multiples of 2, 3, 4, 5 and 6. How do you go about it?
2 = 2, 4, 6, 8, 10, 12, 14,
16, 18 and 20
3 = 3, 6, 9, 12, 15, 18, 21,
24, 27, and 30
4 = 4, 8, 12, 16, 20, 24,
28, 32, 36 and 40
5 = 5, 10, 15, 20, 25, 30,
35, 40, 45, and 50
6 = 6, 12, 18, 24, 30, 36,
42, 48, 54 and 60
The working above can only
be achieved accurately by multiplying given numbers by integers. A multiple of a number is that number
multiplied by an integer.
Integers
Integers are whole number, 2 is multiplied by 1 to get
2, by 2 to get 4, by 3 to 6 and so on. 1, 2, 3, etc, that 2 is multiplied by
are called integers, they can either be negative or positive so other multiples
of 2 are -2, -4, -6, -8, etc.
Common Multiples
These are numbers that
appears with the multiples of two or more given numbers. The idea of common
multiples should not be prolonged at all. Let take from the examples of
multiples of numbers given above.
2 = 2, 4, 6, 8, 10, 12, 14,
16, 18 and 20
3 = 3, 6, 9, 12, 15, 18, 21,
24, 27, and 30
If a cross checking is
carried out well you will see that; within the multiples of 2 and 3 appears two
or three numbers that are common i.e. 6, 12 and 18. Therefore, the common
multiples of 2 and 3 are 6, 12 and 18.
Least Common Multiples
This simply means the lowest
among the common multiples of two or more given numbers. In order not to
prolong this part, we would take from the examples given above to solve lowest
common multiples. The common multiples of two 2 and 3 are 6, 12 and 18 as
solved above. Which of these multiples is the lowest multiple? I am sure no one will choose 12 or 18. Therefore
if 12 or 18 is not the L. C. M., 6 is the Least Common Multiple amidst the
common multiples of 2 and 3.
The End.
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