LCM of 11 and 16 is 176. The smallest number among all common multiples of 11 and 16 is the LCM of 11 and 16. (11, 22, 33, 44,…) and (16, 32, 48, 64, 80, 96,…) are the first few multiples of 11 and 16, respectively. To find the LCM of 11 and 16, there are three typical methods: division, prime factorization, and listing multiples. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 11 and 16?
The answer to this question is 176. The LCM of 11 and 16 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 11 and 16, is the smallest positive integer 176 which is divisible by both 11 and 16 with no remainder.
How to Find LCM of 11 and 16?
LCM of 11 and 16 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 11 and 16 Using Prime Factorisation Method
The prime factorisation of 11 and 16, respectively, is given by:
(11) = 111 and
16 = (2 × 2 × 2 × 2) = 24
LCM (11, 16) = 176
LCM of 11 and 16 Using Division Method
We’ll divide the numbers (11, 16) by their prime factors to get the LCM of 11 and 16 using the division method (preferably common). The LCM of 11 and 16 is calculated by multiplying these divisors.
| 2 | 11 | 16 |
| 2 | 11 | 8 |
| 2 | 11 | 4 |
| 2 | 11 | 2 |
| 11 | 11 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (11, 16) = 176
LCM of 11 and 16 Using Listing the Multiples
To calculate the LCM of 11 and 16 by listing out the common multiples, list the multiples as shown below
| Multiples of 11 | Multiples of 16 |
| 11 | 36 |
| 22 | 32 |
| 33 | 48 |
| ….. | …. |
| 176 | 176 |
The smallest common multiple of 11 and 16 is 176.
Therefore LCM (11, 16) = 176
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LCM of 11 and 16 Solved Example
The GCD and LCM of two numbers are 1 and 176 respectively. If one number is 11, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 11 × z
⇒ z = (GCD × LCM)/11
⇒ z = (1 × 176)/11
⇒ z = 16
Therefore, the other number is 16.
Frequently Asked Questions on LCM of 11 and 16
What is the LCM of 11 and 16?
List the methods used to find the LCM of 11 and 16.
If the LCM of 16 and 11 is 176, Find its GCF.
Since the LCM of 16 and 11 = 176
⇒ 176 × GCF(16, 11) = 176
Therefore, the GCF (greatest common factor) = 176/176 = 1.
What is the Relation Between GCF and LCM of 11, 16?
What is the Least Perfect Square Divisible by 11 and 16?
LCM of 11 and 16 = 2 × 2 × 2 × 2 × 11 [Incomplete pair(s): 11] ⇒ Least perfect square divisible by each 11 and 16 = LCM(11, 16) × 11 = 1936 [Square root of 1936 = √1936 = ±44] Therefore, 1936 is the required number.
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