LCM of 16, 18 and 24 is 144. LCM (Least Common Multiple or Lowest common multiple), is the smallest and the least positive integer that is a common multiple for a given set of numbers. Consider the example for finding the LCM of 16, 18 and 24. The answer is 144. 144 is divisible by 16, 18 and 24. Even 288 is divisible by 16, 18 and 24, however it is not the LCM for 16, 18 and 24. The smaller number than 288 is 144 which is divisible by 16, 18 and 24. Hence 144 is the Least Common Multiple for 16, 18 and 24. You can refer to LCM for more details.
What is LCM of 16, 18 and 24
The Least Common Multiple or Lowest Common Multiple of 16, 18 and 24 is 144.
How to Find LCM of 16, 18 and 24?
LCM of 16, 18 and 24 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16, 18 and 24 Using Prime Factorisation Method
In the Prime Factorisation method, 16, 18 and 24 can be expressed as;
16 = 2 × 2 × 2 × 2
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
By considering the prime factors from each number and not repeating it multiple times, their product forms the LCM.
Therefore, LCM (16, 18 and 24) = 2 × 2 × 2 × 2 × 3 × 3 = 144
LCM of 16, 18 and 24 Using Division Method
In the Division Method, we divide 16, 18 and 24 with 2 as all are even numbers. The division to be completed with remainders as 1 for all 3 numbers. This is achieved by increasing the prime divisors. Product of the prime divisors form the LCM.
Steps shown below;
|
2 |
16 |
18 |
24 |
|
2 |
8 |
9 |
12 |
|
2 |
4 |
9 |
6 |
|
2 |
2 |
9 |
3 |
|
3 |
1 |
9 |
3 |
|
3 |
1 |
3 |
1 |
|
× |
1 |
1 |
1 |
LCM (16, 18 and 24) = 2 × 2 × 2 × 2 × 3 × 3 = 144
LCM of 16, 18 and 24 Using Listing the Multiples
By listing all the multiples of 16, 18 and 24, we can see the least common multiple, which is the LCM. Below is the list of multiples for 16, 18 and 24
|
Multiples of 16 |
Multiples of 18 |
Multiples of 24 |
|
16 |
18 |
24 |
|
32 |
36 |
48 |
|
48 |
54 |
72 |
|
64 |
72 |
120 |
|
80 |
90 |
144 |
|
96 |
108 |
168 |
|
112 |
126 |
192 |
|
128 |
144 |
216 |
|
144 |
162 |
240 |
LCM (16, 18 and 24) = 144
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 16, 18 and 24?
Answer: 144 is the smallest number that is divisible by 16, 18 and 24.
What is the LCM for 4 and 144?
Answer: LCM for 4 and 144 is 144.
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