LCM of 14 and 16 is 112. Get to know how the least common multiple of 14 and 16 is obtained by taking the common multiples into consideration. The multiples of 14 are (14, 28, 42, 56, ….) and the multiples of 16 are (16, 32, 48, 64, 80,….). You can find the LCM of two numbers using the prime factorisation method, by listing out the multiples and division methods.
Also read: Least common multiple
What is LCM of 14 and 16?
The answer to this question is 112. The LCM of 14 and 16 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 14 and 16, is the smallest positive integer 112 which is divisible by both 14 and 16 with no remainder.
How to Find LCM of 14 and 16?
LCM of 14 and 16 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 16 Using Prime Factorisation Method
The prime factorisation of 14 and 16, respectively, is given by:
14 = 2 x 7 = 2¹ x 7¹
16 = 2 x 2 x 2 x 2 = 2⁴
LCM (14, 16) = 112
LCM of 14 and 16 Using Division Method
We’ll divide the numbers (14, 16) by their prime factors to get the LCM of 14 and 16 using the division method (preferably common). The LCM of 14 and 16 is calculated by multiplying these divisors.
| 2 | 14 | 16 |
| 2 | 7 | 8 |
| 2 | 7 | 4 |
| 2 | 7 | 2 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (14, 16) = 112
LCM of 14 and 16 Using Listing the Multiples
To calculate the LCM of 14 and 16 by listing out the common multiples, list the multiples as shown below
| Multiples of 14 | Multiples of 16 |
| 14 | 16 |
| 28 | 72 |
| 42 | 48 |
| 56 | 64 |
| 70 | 80 |
| 84 | 96 |
| 98 | 112 |
| 112 | 128 |
| 126 | 144 |
The smallest common multiple of 14 and 16 is 112.
Therefore LCM (14, 16) = 112
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LCM of 14 and 16 Solved Example
Question: If the product of two numbers is 224 and the GCD is 2, determine the LCM.
Solution:
It is given that
Product of two numbers = 224
GCD = 2
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 224/2
LCM = 112
Hence, the LCM is 112.
Frequently Asked Questions on LCM of 14 and 16
What is the LCM of 14 and 16?
Write the methods used to get the LCM of 14 and 16.
Determine the GCF if the LCM of 14 and 16 is 112.
LCM x GCF = 14 x 16
Given
LCM of 14 and 16 = 112
112 x GCF = 224
GCF = 224/112 = 2
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