LCM of 7 and 16 is 112. 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 7 and 16, the LCM of 7 and 16 is the smallest value. (7, 14, 21, 28, 35, 42, 49, etc.) and (16, 32, 48, 64, 80, 96, etc.) are the first several multiples of 7 and 16, respectively. 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 7 and 16?
The answer to this question is 112. The LCM of 7 and 16 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 7 and 16, is the smallest positive integer 112 which is divisible by both 7 and 16 with no remainder.
How to Find LCM of 7 and 16?
LCM of 7 and 16 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7 and 16 Using Prime Factorisation Method
The prime factorisation of 7 and 16, respectively, is given by:
(7) = 71 and
16 = (2 × 2 × 2 × 2) = 24
LCM (7, 16) = 112
LCM of 7 and 16 Using Division Method
We’ll divide the numbers (7, 16) by their prime factors to get the LCM of 7 and 16 using the division method (preferably common). The LCM of 7 and 16 is calculated by multiplying these divisors.
| 2 | 7 | 16 |
| 2 | 7 | 8 |
| 2 | 7 | 4 |
| 2 | 7 | 2 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (7, 16) = 112
LCM of 7 and 16 Using Listing the Multiples
To calculate the LCM of 7 and 16 by listing out the common multiples, list the multiples as shown below.
| Multiples of 7 | Multiples of 16 |
| 7 | 16 |
| 14 | 32 |
| 21 | 48 |
| 28 | 64 |
| 35 | 80 |
| ….. | 96 |
| 112 | 112 |
The smallest common multiple of 7 and 16 is 112.
Therefore LCM (7, 16) = 112
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LCM of 7 and 16 Solved Examples
Question: Find the smallest number that is divisible by 7 and 16 exactly.
Solution:
The value of LCM(7, 16) will be the smallest number that is exactly divisible by 7 and 16.
⇒ Multiples of 7 and 16
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 91, 98, 105, 112, . . . .
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 48, 64, 80, 96, 112, . . . .
Therefore, the LCM of 7 and 16 is 112.
Frequently Asked Questions on LCM of 7 and 16
What is the LCM of 7 and 16?
List the methods used to find the LCM of 7 and 16.
What is the Relation Between GCF and LCM of 7, 16?
If the LCM of 16 and 7 is 112, Find its GCF.
Since the LCM of 16 and 7 = 112
⇒ 112 × GCF(16, 7) = 112
Therefore, the GCF (greatest common factor) = 112/112 = 1.
How to Find the LCM of 7 and 16 by Prime Factorization?
⇒ LCM of 7, 16 = 24 × 7 = 112.
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