The Least Common Multiple of 2 and 7 is 14. This is the smallest number that both 2 and 7 can divide into evenly. Therefore, 14 is their Least Common Multiple or LCM. You can find more examples and explanations on the LCM with Examples page.
LCM of 2 and 7 - Definition, Methods and Examples | Testbook.com
Last Updated on Jun 07, 2024
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Understanding the LCM of 2 and 7
The Lowest Common Multiple (LCM) of 2 and 7 is none other than 14.
Methods to Find the LCM of 2 and 7
The LCM of 2 and 7 can be found using three different methods:
- Prime Factorisation
- Division method
- Listing the multiples
Prime Factorisation Method for LCM of 2 and 7
The Prime Factorisation method involves breaking down the numbers into their prime factors. For 2 and 7, we have:
2 = 2 x 1
7 = 7 x 1
Therefore, LCM (2, 7) = 2 x 7 = 14
Division Method for LCM of 2 and 7
The Division Method involves dividing the numbers by the smallest number that can divide them both evenly until we can't divide further or only prime numbers are left.
| 2 | 2 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
Hence, LCM (2, 7) = 2 x 7 = 14
Listing the Multiples for LCM of 2 and 7
By listing the multiples of 2 and 7, we can find the least number they both share - which is the LCM. Here are the multiples for 2 and 7:
| Multiples of 2 | Multiples of 7 |
| 2 | 7 |
| 4 | 14 |
| 6 | 21 |
| 8 | 28 |
| 10 | 35 |
| 12 | 42 |
| 14 | 49 |
Therefore, LCM (2, 7) = 14
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Examples
- What is the smallest number that can be divided evenly by both 3 and 8?
Answer: The smallest number that is divisible by both 3 and 8 is 24.
2. What is the Highest Common Factor for 5 and 10?
Answer: The Highest Common Factor for 5 and 10 is 5.
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Frequently Asked Questions
What is the LCM of 2 and 7?
The LCM of 2 and 7 is 14.
Is the LCM of 2 and 7 the same as the HCF of 2 and 7?
No. The Least Common Multiple of 2 and 7 is 14 and the Highest Common Factor of 2 and 7 is 1.
What is the common factor of 2 and 7?
1 is the common factor of 2 and 7.