LCM of 15 and 21 is 105.The smallest number among all common multiples of 15 and 21 is the LCM of 15 and 21. (15, 30, 45, 60, 75, 90, etc.) and (21, 42, 63, 84, 105, 126, etc.) are the first few multiples of 15 and 21. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 15 and 21?
The answer to this question is 105. The LCM of 15 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 15 and 21, is the smallest positive integer 105 which is divisible by both 15 and 21 with no remainder. LCM of 15 and 21 is the smallest number among all common multiples of 15 and 21. The first few multiples of 15 and 21 are (15, 30, 45, 60, 75, 90, . . . ) and (21, 42, 63, 84, 105, 126, . . . ) respectively.
How to Find LCM of 15 and 21?
LCM of 15 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 21 Using Prime Factorisation Method
The prime factorisation of 15 and 21, respectively, is given by:
15 = (3 × 5) = 31 × 51 and
21 = (3 × 7) = 31 × 71
LCM (15, 21) = 105
LCM of 15 and 21 Using Division Method
We’ll divide the numbers (15, 21) by their prime factors to get the LCM of 15 and 21 using the division method (preferably common). The LCM of 15 and 21 is calculated by multiplying these divisors.
| 3 | 15 | 21 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (15, 21) = 105
LCM of 15 and 21 Using Listing the Multiples
To calculate the LCM of 15 and 21 by listing out the common multiples, list the multiples as shown below.
| Multiples of 15 | Multiples of 21 |
| 15 | 21 |
| 30 | 42 |
| 45 | 63 |
| 60 | 84 |
| 75 | 105 |
| 90 | – |
| 105 | – |
The smallest common multiple of 15 and 21 is 105.
Therefore LCM (15, 21) = 105
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LCM of 15 and 21 Solved Example
Question: The product of two numbers is 315. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 315
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 315/3
Therefore, the LCM is 105.
The probable combination for the given case is LCM(15, 21) = 105.
Frequently Asked Questions on LCM of 15 and 21
What is the LCM of 15 and 21?
List the methods used to find the LCM of 15 and 21.
If the LCM of 21 and 15 is 105, Find its GCF.
Since the LCM of 21 and 15 = 105
⇒ 105 × GCF(21, 15) = 315
Therefore, the GCF = 315/105 = 3.
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