LCM of 4, 8 and 16 is 16. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all common multiples of 4, 8, and 16 is the LCM of 4, 8, and 16. (4, 8, 12, 16, 20…), (8, 16, 24, 32, 40…), and (16, 32, 48, 64, 80…), correspondingly, are the first few multiples of 4, 8, and 16. There are three typical ways for calculating the LCM of 4, 8 and 16: division, prime factorization, and listing multiples.
Also read: Least common multiple
What is LCM of 4, 8 and 16?
The answer to this question is 16. The LCM of 4, 8 and 16 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 8 and 16, is the smallest positive integer 16 which is divisible by both 4, 8 and 16 with no remainder.
How to Find LCM of 4, 8 and 16?
LCM of 4, 8 and 16 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4, 8 and 16 Using Prime Factorisation Method
The prime factorisation of 4, 8 and 16, respectively, is given by:
4 = (2 × 2) = 22,
8 = (2 × 2 × 2) = 23, and
16 = (2 × 2 × 2 × 2) = 24
LCM (4, 8, 16) = 16
LCM of 4, 8 and 16 Using Division Method
We’ll divide the numbers (4, 8, 16) by their prime factors to get the LCM of 4, 8 and 16 using the division method (preferably common). The LCM of 4, 8 and 16 is calculated by multiplying these divisors.
|
2 |
4 |
8 |
16 |
|
2 |
2 |
4 |
8 |
|
2 |
1 |
2 |
4 |
|
2 |
1 |
1 |
2 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (4, 8, 16) = 16
LCM of 4, 8 and 16 Using Listing the Multiples
To calculate the LCM of 4, 8 and 16 by listing out the common multiples, list the multiples as shown below
|
Multiples of 4 |
Multiples of 8 |
Multiples of 16 |
|
4 |
8 |
16 |
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8 |
16 |
32 |
|
12 |
24 |
48 |
|
16 |
32 |
64 |
|
20 |
40 |
80 |
The smallest common multiple of 4, 8 and 16 is 16.
LCM (4, 8, 16) = 16
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Video Lesson on Applications of LCM
LCM of 4, 8 and 16 Solved Example
Find the smallest number that is divisible by 4, 8, 16 exactly.
Solution:
The smallest number that is divisible by 4, 8, and 16 exactly is their LCM.
⇒ Multiples of 4, 8, and 16:
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, . . . .
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, . . . .
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, . . . .
Therefore, the LCM of 4, 8, and 16 is 16.
Frequently Asked Questions on LCM of 4, 8 and 16
What is the LCM of 4, 8 and 16?
List the methods used to find the LCM of 4, 8 and 16.
What is the Least Perfect Square Divisible by 4, 8, and 16?
LCM of 4, 8, and 16 = 2 × 2 × 2 × 2 [No incomplete pair] ⇒ Least perfect square divisible by each 4, 8, and 16 = LCM(4, 8, 16) = 16 [Square root of 16 = √16 = ±4] Therefore, 16 is the required number.
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