LCM of 14 and 35 is 70. In Maths, the full form of LCM is the least common multiple. Students can learn the LCM of given numbers with examples by referring to the article Least Common Multiple (LCM) prepared by expert faculty in a simple language. Prime factorisation, division method and listing multiples are the three methods to find the LCM of two or more numbers. Let us learn how to determine the least common multiple of 14 and 35 using prime factorisation, division method and listing multiples in a clear format in this article.
What is LCM of 14 and 35?
The answer to this question is 70.
How to Find LCM of 14 and 35?
The below methods are used to find the LCM of 14 and 35:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 35 Using Prime Factorisation Method
By prime factorisation method, we can write 14 and 35 as the product of prime numbers, such that;
14 = 2 × 7
35 = 5 × 7
LCM (14, 35) = 2 × 5 × 7 = 70
LCM of 14 and 35 Using Division Method
Here, to find the LCM, we divide the numbers 14 and 35 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 14 and 35.
| 2 | 14 | 35 |
| 5 | 7 | 35 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (14, 35) = 2 × 5 × 7 = 70
LCM of 14 and 35 Using Listing the Multiples
To find the least common multiple of 14 and 35 using listing multiples, we list out the multiples of 14 and 35. The multiples of 14 and 35 are shown in the below table.
| Multiples of 14 | Multiples of 35 |
|
14 |
35 |
| 28 | 70 |
| 42 | 105 |
| 56 | 140 |
| 70 | 175 |
| 84 | 210 |
LCM (14, 35) = 70
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: The GCD and LCM of two numbers are 7 and 70. If one number is 14, calculate the other number.
Solution: Let the other number be p.
We know that,
GCD × LCM = 14 × p
p = (GCD × LCM) / 14
p = (7 × 70) / 14
p = 35
Hence, the other number is 35.
Q. 2: Find the LCM of 14 and 35 using division method.
Solution: We can represent the LCM of 14 and 35 using division method as below
| 2 | 14 | 35 |
| 5 | 7 | 35 |
| 7 | 7 | 7 |
| x | 1 | 1 |
LCM (14, 35) = 2 × 5 × 7 = 70
Therefore the least common multiple of 14 and 35 by division method is 70.
Comments