LCM of 8 and 14 is 56. The top-grade faculty with good knowledge of the LCM concept curated the article LCM of Two Numbers in a clear format based on the understanding abilities of students. Referring to this article in detail, students get to learn how to find the least common multiple of two numbers more effectively. Grasping the LCM concept thoroughly enables students to answer tricky questions in exams easily. Let us glance at how to find the least common multiple of 8 and 14 in a simple process in this article.
What is LCM of 8 and 14?
The Least Common Multiple of 8 and 14 is 56.
How to Find LCM of 8 and 14?
The methods used to find the LCM of 8 and 14 are:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 14 Using Prime Factorisation Method
By prime factorisation method, we can write 8 and 14 as the product of prime numbers, such that;
8 = 2 × 2 × 2
14 = 2 × 7
LCM (8, 14) = 2 × 2 × 2 × 7 = 56
LCM of 8 and 14 Using Division Method
In this method, to calculate the LCM, we divide the numbers 8 and 14 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 8 and 14. This can be shown as below.
| 2 | 8 | 14 |
| 2 | 4 | 7 |
| 2 | 2 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (8, 14) = 2 × 2 × 2 × 7 = 56
LCM of 8 and 14 Using Listing the Multiples
Here, we list out the multiples of 8 and 14 to find their least common multiple. The following tables give the multiples of 8 and 14.
| Multiples of 8 | Multiples of 14 |
| 8 | 14 |
| 16 | 28 |
| 24 | 42 |
| 32 | 56 |
| 40 | 70 |
| 48 | 84 |
| 56 | 98 |
| 64 | 112 |
LCM (8, 14) = 56
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 8 and 14?
Solution: 56 is the smallest number that is divisible by both 8 and 14.
Q. 2: Find the LCM of 8 and 14 using listing multiples.
Solution: First, list the multiples of 8 and 14
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, …….
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, …..
Here the least common multiple is 56
Therefore the LCM of 8 and 14 by listing multiples is 56.
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