LCM of 8, 9 and 25 is 1800. The Least Common Divisor (LCD) also known as Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 8, 9 and 25, 1800 is the first(least or smallest) number that is common in the set of multiples of 8, 9 and 25. 3600, 5400, 7200, .. are also common multiples, however 1800 is the LCM. You can refer to Multiples.
What is LCM of 8, 9 and 25
The Least Common Multiple or Lowest Common Multiple of 8, 9 and 25 is 1800.
How to Find LCM of 8, 9 and 25?
LCM of 8, 9 and 25 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 9 and 25 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 8, 9 and 25 can be expressed as;
8 = 2 × 2 × 2
9 = 3 × 3
25 = 5 × 5
The common and uncommon prime factors of 8, 9 and 25 and its product is the LCM
LCM(8, 9 and 25) = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800
LCM of 8, 9 and 25 Using Division Method
In the Division Method, the given set of numbers 8, 9 and 25 are divided by the prime factors, starting from the first prime factor and by increasing till the remainders are 1 for all three. The product of these prime factors is the LCM.
|
2 |
8 |
9 |
25 |
|
2 |
4 |
9 |
25 |
|
2 |
2 |
9 |
25 |
|
3 |
1 |
9 |
25 |
|
3 |
1 |
3 |
25 |
|
5 |
1 |
1 |
25 |
|
5 |
1 |
1 |
5 |
|
× |
1 |
1 |
1 |
LCM (8, 9 and 25) = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800
LCM of 8, 9 and 25 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 8, 9 and 25
Multiples of 8
8, 16, …104, 112, 120, …408, 416, 424..1008, 1016, …1512, 1520, 1528, .. 1784, 1792, 1800..
Multiples of 9
9, 18, 27…, 108, 117, 126…702, 711, 720.. 1008, 1017, … 1440, 1449, 1458, .., 1746, 1755, ..1791, 1800,
Multiples of 25
25, 50, …125, 150, …, 875, 900, 925, ..1425, 1450, 1475, 1500, … 1750, 1775, 1800, 1825
LCM (8, 9 and 25) = 1800
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 8, 9 and 25?
Answer: 1800 is the smallest number that is divisible by 8, 9 and 25.
What is the LCM of 20 and 1800?
Answer: LCM of 20 and 1800 is 1800.
Comments