LCM of 36 and 100 is 900. LCM stands for the Least Common Multiple or Lowest Common Multiple. LCM is the first positive numeral that is divisible by the given numbers. In the given set of numbers 36 and 100, 900 is the first(least or smallest) number that is common in the set of common multiples of 36 and 100. The LCM which is also known as LCD, Least Common Divisor for 36 and 100 is 900. You can read more on LCM for further details.
What is LCM of 36 and 100
The Least Common Multiple or Lowest Common Multiple of 36 and 100 is 900.
How to Find LCM of 36 and 100?
LCM of 36 and 100 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 100 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 36 and 100 can be expressed as;
36 = 2 × 2 × 3 × 3
100 = 2 × 2 × 5 × 5
The common prime factors (2 × 2) are multiplied by uncommon prime factors (3 × 3 × 5 × 5) which forms the LCM.
LCM (36, 100) = 2 × 2 × 3 × 3 × 5 × 5 = 900
LCM of 36 and 100 Using Division Method
In the Division Method for 36 and 100,
- Using prime divisors, divide 36 and 100
- Multiply the prime divisors to get the LCM.
Both steps shown in the table below;
|
2 |
36 |
100 |
|
2 |
18 |
50 |
|
3 |
9 |
25 |
|
3 |
3 |
25 |
|
5 |
1 |
25 |
|
5 |
1 |
5 |
|
× |
1 |
1 |
Therefore LCM (36, 100) = 2 × 2 × 3 × 3 × 5 × 5 = 900
LCM of 36 and 100 Using Listing the Multiples
By listing all the multiples of 36 and 100, we can pick the first common multiple, which is the LCM. Below is the list of multiples for 36 and 100
Multiples of 36
36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972
Multiples of 100
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100
LCM (36, 100) = 900
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 36 and 100?
Answer: 900 is the smallest number that is divisible by both 36 and 100.
What is the LCM for 6, 36 and 100?
Answer: LCM for 6, 36 and 100 is 900 as 6 is the factor of 36 and 100.
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