What are Multiples of 36?
When the number 36 is multiplied by any natural number, such as 1, 2, 3, and so on, the resulting product is known as a multiple of 36.
For example: If we multiply 36 by 5, then the product is 180. As a result, we can define 180 as a multiple of 36 as well as a multiple of 5.
The multiples of 36 can be written as \(36n \) where n is a natural number, \(n \) = 1, 2, 3, 4, 5, 6, ….
The multiples of 36 will be: 36, 72, 108, 144, 180, 216, 252, 288, …
Also, we can observe that the difference between consecutive multiples of 36, that is, the difference between each succeeding and preceding multiple of 36 is 36:
72 – 36 = 36,
108 – 72 = 36,
144 – 108 = 36, and so on.
For example: 180, 216 and 252 are all multiples of 36 because we can get these numbers by multiplying 36 with a natural number.
36 × 5 = 180 | 36 is multiplied by 5 to get 180 |
36 × 6 = 216 | 36 is multiplied by 6 to get 216 |
36 × 7 = 252 | 36 is multiplied by 7 to get 252 |
Finding the Multiples of 36 by Repeated Addition
Repeated addition means adding a number to itself, multiple times. We can use repeated addition to find the multiples of a number.
Let’s find the first 10 multiples of 36:
36 \(\times \) 1 = 36 | 36 | |
36 \(\times \) 2 = 72 | 36 + 36 = 72 | Here 36 is added two times |
36 \(\times \) 3 = 108 | 36 + 36 + 36 = 108 | Here 36 is added three times |
36 \(\times \) 4 = 144 | 36 + 36 + 36 + 36 = 144 | Here 36 is added four times |
36 \(\times \) 5 = 180 | 36 + 36 + 36 + 36 + 36 = 180 | Here 36 is added five times |
36 \(\times \) 6 = 216 | 36 + 36 + 36 + 36 + 36 +36 = 216 | Here 36 is added six times |
36 \(\times \) 7 = 252 | 36 + 36 + 36 + 36 + 36 + 36 +36 = 252 | Here 36 is added seven times |
36 \(\times \) 8 = 288 | 36 + 36 + 36 + 36 + 36 +36 + 36 + 36 = 288 | Here 36 is added eight times |
36 \(\times \) 9 = 324 | 36 + 36 + 36 + 36 + 36 +36 + 36 + 36 + 36 = 324 | Here 36 is added nine times |
36 \(\times \) 10 = 360 | 36 + 36 + 36 + 36 + 36 +36 + 36 + 36 + 36 +36 = 360 | Here 36 is added ten times |
Similarly, the nth multiple of 36 can be obtained by either multiplying 36 by \(n \) or by adding \(36 ~n \) times, where \(n \) is any natural number.
Therefore,
The \(36 ~n \)th multiple of 36 = \(36~\times ~n \),
or
\(n \)th multiple of 36 = 36 + 36 + … \(n \) times
Solved Multiples of 36 Examples
Example 1: Is 200 a multiple of 36?
Solution:
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, …
200 is not included in the list.
Also \(\frac{200}{36} \) = 5 R20. When 200 is divided by 36, we get the quotient as 5 and the remainder as 20. Since the remainder is not 0, we can say that 36 is not a factor of 200.
Hence, 200 is not a multiple of 36.
Example 2: What is the 5th multiple of 36?
Solution:
The 5th multiple of 36 can be obtained by the repeated addition of 36 5 times or by multiplying 36 by 5:
So, 36 + 36 +36 + 36 + 36 = 36 \(\times \) 5 = 180
Hence, the 5th multiple of 36 is 180.
Example 3: What is the least common multiple of 12, 24 and 36?
Solution:
The least or lowest common multiple is the smallest multiple that is common to all the given numbers. Hence, the least common multiple of 12, 24 and 36 is the smallest multiple common to 12, 24 and 36.
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ….
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, ….
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, …
From above, we can see that the smallest multiple common in 12, 24 and 36 is 72.
So, the least common multiple of 12, 24 and 36 is 72.
Example 4: Jerry is calculating the area of a triangle whose base is 36 cm and height is 5 times its base. What is the area of the triangle?
Solution:
Base of the triangle = 36 cm
Height of the triangle = 5 times the base
= 5 \(\times \) 36
= 180 cm
Area of the triangle = \(\frac{1}{2}~\times~\text{base}~\times~\text{height} \)
= \(\frac{1}{2}~\times~36~\times~180 \)
= 3240 \(cm^2\)
The multiples of a number are obtained by multiplying a natural number with a natural number. The product thus obtained is a multiple of both the given numbers.
When a natural number is multiplied by another natural number, then the resultant product is a multiple of both the numbers and these numbers that are multiplied are factors of the resultant product.
For example: 7 x 36 = 252
252 is a multiple of both 7 and 36. Also, 7 and 36 are factors of 252.
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48,….
36 is included in the above list.
Also, \(\frac{36}{6}\) = 6 R0. When 36 is divided by 6, the quotient is 6 and the remainder is 0. Hence 6 is a factor of 36.
Additionally, 36 is a multiple of 6.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
There are infinite natural numbers that a number can be multiplied with. So a number can have infinite multiples.