LCM of 8, 12 and 15 is 120. The smallest number among all frequent multiples of 8, 12, and 15 is the LCM of 8, 12, and 15. The first few multiples of 8, 12, and 15 are (8, 16, 24, 32, 40, etc. ), (12, 24, 36, 48, 60, etc.) and (15, 30, 45, 60, 75, etc.). The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. To find the LCM of 8, 12, or 15, you can use one of three methods: prime factorization, division, or listing multiples.
Also read: Least common multiple
What is LCM of 8, 12 and 15?
The answer to this question is 120. The LCM of 8, 12 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 12 and 15, is the smallest positive integer 120 which is divisible by both 8, 12 and 15 with no remainder.
How to Find LCM of 8, 12 and 15?
LCM of 8, 12 and 15 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 12 and 15 Using Prime Factorisation Method
The prime factorisation of 8, 12 and 15, respectively, is given by:
8 = (2 × 2 × 2) = 23,
12 = (2 × 2 × 3) = 22 × 31, and
15 = (3 × 5) = 31 × 51
LCM (8, 12, 15) = 120
LCM of 8, 12 and 15 Using Division Method
We’ll divide the numbers (8, 12, 15) by their prime factors to get the LCM of 8, 12 and 15 using the division method (preferably common). The LCM of 8, 12 and 15 is calculated by multiplying these divisors.
| 2 | 8 | 12 | 15 |
| 2 | 4 | 6 | 15 |
| 2 | 2 | 3 | 15 |
| 3 | 1 | 3 | 15 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (8, 12, 15) = 120
LCM of 8, 12 and 15 Using Listing the Multiples
To calculate the LCM of 8, 12 and 15 by listing out the common multiples, list the multiples as shown below
| Multiples of 8 | Multiples of 12 | Multiples of 15 |
| 8 | 12 | 15 |
| 16 | 24 | 30 |
| 24 | 36 | 45 |
| …. | …. | … |
| 120 | 120 | 120 |
The smallest common multiple of 8, 12 and 15 is 120.
Therefore LCM (8, 12, 15) = 120
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LCM of 8, 12 and 15 Solved Example
Question: Find the smallest number that is divisible by 8, 12, 15 exactly.
Solution:
The smallest number that is divisible by 8, 12, and 15 exactly is their LCM.
⇒ Multiples of 8, 12, and 15:
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, . . . .
Therefore, the LCM of 8, 12, and 15 is 120.
Frequently Asked Questions on LCM of 8, 12 and 15
What is the LCM of 8, 12 and 15?
List the methods used to find the LCM of 8, 12 and 15.
What is the Least Perfect Square Divisible by 8, 12, and 15?
LCM of 8, 12, and 15 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 8, 12, and 15 = LCM(8, 12, 15) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
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