LCM of 16 and 21 is 336. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 16 and 21, the LCM of 16 and 21 is the smallest number. (16, 32, 48, 64, 80, 96, etc.) and (21, 42, 63, 84, 105, 126, 147, etc.) respectively are the first few multiples of 16 and 21. 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 16 and 21?
The answer to this question is 336. The LCM of 16 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 16 and 21, is the smallest positive integer 336 which is divisible by both 16 and 21 with no remainder.
How to Find LCM of 16 and 21?
LCM of 16 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16 and 21 Using Prime Factorisation Method
The prime factorisation of 16 and 21, respectively, is given by:
16 = (2 × 2 × 2 × 2) = 24 and
21 = (3 × 7) = 31 × 71
LCM (16, 21) = 336
LCM of 16 and 21 Using Division Method
We’ll divide the numbers (16, 21) by their prime factors to get the LCM of 16 and 21 using the division method (preferably common). The LCM of 16 and 21 is calculated by multiplying these divisors.
| 2 | 16 | 21 |
| 2 | 8 | 21 |
| 2 | 4 | 21 |
| 2 | 2 | 21 |
| 3 | 1 | 21 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (16, 21) = 336
LCM of 16 and 21 Using Listing the Multiples
To calculate the LCM of 16 and 21 by listing out the common multiples, list the multiples as shown below
| Multiples of 16 | Multiples of 21 |
| 16 | 21 |
| 32 | 42 |
| 48 | 63 |
| ….. | …… |
| 336 | 336 |
The smallest common multiple of 16 and 21 is 336.
Therefore LCM (16, 21) = 336
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LCM of 16 and 21 Solved Example
The GCD and LCM of two numbers are 1 and 336 respectively. If one number is 16, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 16 × z
⇒ z = (GCD × LCM)/16
⇒ z = (1 × 336)/16
⇒ z = 21
Therefore, the other number is 21.
Frequently Asked Questions on LCM of 16 and 21
What is the LCM of 16 and 21?
List the methods used to find the LCM of 16 and 21.
Which of the following is the LCM of 16 and 21? 15, 2, 42, 336
If the LCM of 21 and 16 is 336, Find its GCF.
Since the LCM of 21 and 16 = 336
⇒ 336 × GCF(21, 16) = 336
Therefore, the GCF = 336/336 = 1.
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