LCM of 12, 16 and 20 is 240. The smallest number among all common multiples of 12, 16, and 20 is the LCM of 12, 16, and 20. (12, 24, 36, 48, 60…), (16, 32, 48, 64, 80…), and (20, 40, 60, 80, 100…), respectively, are the first few multiples of 12, 16, and 20. To find the LCM of 12, 16, or 20, there are three typical methods: listing multiples, division method, and prime factorization. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 12, 16 and 20?
The answer to this question is 240. The LCM of 12, 16 and 20 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12, 16 and 20, is the smallest positive integer 240 which is divisible by both 12, 16 and 20 with no remainder.
How to Find LCM of 12, 16 and 20?
LCM of 12, 16 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 16 and 20 Using Prime Factorisation Method
The prime factorisation of 12, 16 and 20, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31,
16 = (2 × 2 × 2 × 2) = 24, and
20 = (2 × 2 × 5) = 22 × 51
LCM (12, 16, 20) = 240
LCM of 12, 16 and 20 Using Division Method
We’ll divide the numbers (12, 16, 20) by their prime factors to get the LCM of 12, 16 and 20 using the division method (preferably common). The LCM of 12, 16 and 20 is calculated by multiplying these divisors.
| 2 | 12 | 16 | 20 |
| 2 | 6 | 8 | 10 |
| 2 | 3 | 4 | 5 |
| 2 | 3 | 2 | 5 |
| 3 | 3 | 1 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (12, 16, 20) = 240
LCM of 12, 16 and 20 Using Listing the Multiples
To calculate the LCM of 12, 16 and 20 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 16 | Multiples of 20 |
| 12 | 16 | 20 |
| 24 | 32 | 40 |
| 36 | 48 | 60 |
| 48 | 64 | 80 |
| … | …. | 100 |
| 120 | 120 | 120 |
The smallest common multiple of 12, 16 and 20 is 72.
Therefore LCM (12, 16, 20) = 120
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LCM of 12, 16 and 20 Solved Example
Question: Find the smallest number that is divisible by 12, 16, 20 exactly.
Solution:
The value of LCM(12, 16, 20) will be the smallest number that is exactly divisible by 12, 16, and 20.
⇒ Multiples of 12, 16, and 20:
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 204, 216, 228, 240, . . . .
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 192, 208, 224, 240, . . . .
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, . . . ., 200, 220, 240, . . . .
Therefore, the LCM of 12, 16, and 20 is 240.
Frequently Asked Questions on LCM of 12, 16 and 20
What is the LCM of 12, 16 and 20?
List the methods used to find the LCM of 12, 16 and 20.
How to Find the LCM of 12, 16, and 20 by Prime Factorization?
⇒ LCM of 12, 16, 20 = 24 × 3 × 5 = 240.
Which of the following is the LCM of 12, 16, and 20? 21, 50, 11, 240
What is the Least Perfect Square Divisible by 12, 16, and 20?
LCM of 12, 16, and 20 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5] ⇒ Least perfect square divisible by each 12, 16, and 20 = LCM(12, 16, 20) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
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