LCM of 12, 15 and 21 is 420. The smallest number among all common multiples of 12, 15, and 21 is the LCM of 12, 15, and 21. (12, 24, 36, 48, 60…), (15, 30, 45, 60, 75…), and (21, 42, 63, 84, 105…), respectively, are the first few multiples of 12, 15, and 21. Students can use the methods such as division, prime factorisation and listing of multiples to get the LCM value.
Also read: Least common multiple
What is LCM of 12, 15 and 21?
The answer to this question is 420. The LCM of 12, 15 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12, 15 and 21, is the smallest positive integer 420 which is divisible by both 12, 15 and 21 with no remainder.
How to Find LCM of 12, 15 and 21?
LCM of 12, 15 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 15 and 21 Using Prime Factorisation Method
The prime factorisation of 12, 15 and 21, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31,
15 = (3 × 5) = 31 × 51, and
21 = (3 × 7) = 31 × 71
LCM (12, 15, 21) = 420
LCM of 12, 15 and 21 Using Division Method
We’ll divide the numbers (12, 12, 21) by their prime factors to get the LCM of 12, 15 and 21 using the division method (preferably common). The LCM of 12, 15 and 21 is calculated by multiplying these divisors.
| 2 | 12 | 15 | 21 |
| 2 | 6 | 15 | 21 |
| 3 | 3 | 15 | 21 |
| 5 | 1 | 5 | 7 |
| 7 | 1 | 1 | 7 |
| 1 | 1 | 1 |
No further division can be done.
Hence, LCM (12, 15, 21) = 420
LCM of 12, 15 and 21 Using Listing the Multiples
To calculate the LCM of 12, 15 and 21 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 15 | Multiples of 21 |
| 12 | 15 | 21 |
| 24 | 30 | 42 |
| 36 | 45 | 63 |
| 48 | 60 | 84 |
| 60 | 75 | 105 |
| 72 | 90 | 126 |
| . | . | . |
| . | . | . |
| 420 (35th multiple) | 420 (28th multiple) | 420 (20th multiple) |
The smallest common multiple of 12, 15 and 21 is 420.
LCM (12, 15, 21) = 420
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LCM of 12, 15 and 21 Solved Examples
Question: Find the smallest number that is divisible by 12, 15, 21 exactly.
Solution:
The value of LCM(12, 15, 21) will be the smallest number that is exactly divisible by 12, 15, and 21.
⇒ Multiples of 12, 15, and 21:
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 396, 408, 420, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 390, 405, 420, . . . .
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 357, 378, 399, 420, . . . .
Therefore, the LCM of 12, 15, and 21 is 420.
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