The Least Common Multiple (LCM) of 10 and 35 is 70. The LCM is a technique used to find the smallest common multiple between two or more numbers. To help students grasp this concept easily, an article titled "Understanding LCM with Examples" has been prepared in a simple and easy-to-understand language. Reading such expert-curated articles on a regular basis can help students enhance their problem-solving skills related to LCM. This article will guide you through the process of finding the LCM of 10 and 35 in simple steps.
LCM of 10 and 35 | How to Find LCM of 10 and 35? | Testbook.com
Last Updated on Jun 10, 2024
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What is the LCM of 10 and 35?
The Least Common Multiple of 10 and 35 is 70.
How to Determine the LCM of 10 and 35?
The LCM of 10 and 35 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
Finding the LCM of 10 and 35 Using Prime Factorisation Method
The prime factorisation method involves multiplying the prime factors, each raised to their highest power, to obtain the LCM of 10 and 35.
10 = 2 × 5
35 = 5 × 7
LCM (10, 35) = 2 × 5 × 7 = 70
Finding the LCM of 10 and 35 Using Division Method
In the division method, we divide the numbers 10 and 35 by their prime factors until we get 1 in the entire row. The product of these divisors gives us the LCM of 10 and 35.
| 2 | 10 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division is possible.
Hence, LCM (10, 35) = 2 × 5 × 7 = 70
Finding the LCM of 10 and 35 by Listing the Multiples
In this method, we list the multiples of 10 and 35 and find the least common multiple among them. The table below shows the multiples of 10 and 35.
| Multiples of 10 | Multiples of 35 |
| 10 | 35 |
| 20 | 70 |
| 30 | 105 |
| 40 | 140 |
| 50 | 175 |
| 60 | 210 |
| 70 | 245 |
| 80 | 280 |
LCM (10, 35) = 70
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Frequently Asked Questions
What is the LCM of 10 and 35?
The LCM of 10 and 35 is 70.
Mention the LCM of 10 and 35 and the HCF of 10 and 35.
The LCM of 10 and 35 is 70 and the HCF of 10 and 35 is 5.
Name the methods used to find the LCM of 10 and 35.
The methods used to find the LCM of 10 and 35 are Prime Factorisation, Division Method, and Listing the Multiples.
Find the GCF if the LCM of 10 and 35 is 70.
The GCF is 5 if the LCM of 10 and 35 is 70.
Calculate the LCM of 10 and 35 using prime factorisation.
In prime factorisation, 10 = 2 × 5, 35 = 5 × 7. Therefore, LCM (10, 35) = 2 × 5 × 7 = 70.
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