LCM of 10 and 35 is 70. The LCM is the method to find the least common multiple between any two or more numbers. The teachers prepared the article LCM with Examples in simple and understandable language so that students could learn the LCM concept easily, irrespective of their intelligence quotient. Following the article curated by experts on a daily basis improves skills of solving the problems based on the LCM with ease. In this article, we will learn how to verify the least common multiple of 10 and 35 with simple steps.
What is LCM of 10 and 35?
The Least Common Multiple of 10 and 35 is 70.
How to Find LCM of 10 and 35?
LCM of 10 and 35 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 10 and 35 Using Prime Factorisation Method
In the prime factorisation method, LCM of 10 and 35 can be obtained by multiplying prime factors raised to their respective highest power.
10 = 2 × 5
35 = 5 × 7
LCM (10, 35) = 2 × 5 × 7 = 70
LCM of 10 and 35 Using Division Method
In the division method, to determine the least common multiple of 10 and 35, we divide the numbers 10 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 10 and 35.
| 2 | 10 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 35) = 2 × 5 × 7 = 70
LCM of 10 and 35 Using Listing the Multiples
In this method, we list down the multiples of 10 and 35 to find the least common multiple among them. The below table 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
Related Articles
- Least Common Multiple (LCM)
- Prime Factorisation and Division Method for LCM and HCF
- LCM of Two Numbers
- HCF and LCM
- LCM calculator
- LCM Formula
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 10 and 35?
Solution: 70 is the smallest number that is divisible by both 10 and 35.
2. What is the LCM if the product of two numbers is 350 and their GCD is 5?
Solution: Given,
GCD = 5
Product of numbers = 350
We know that;
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 350 / 5
LCM = 70
Therefore the LCM is 70.
Frequently Asked Questions on LCM of 10 and 35
What is the LCM of 10 and 35?
Mention the LCM of 10 and 35 and the HCF of 10 and 35.
Name the methods used to find the LCM of 10 and 35.
The methods used to find the LCM of 10 and 35 are as follows:
Prime Factorisation
Division method
Listing the Multiples
Find the GCF if the LCM of 10 and 35 is 70.
GCF × LCM = 10 × 35
Given
LCM = 70
GCF × 70 = 10 × 35
GCF = 5
Calculate the LCM of 10 and 35 using prime factorisation.
In prime factorisation, the given numbers are expressed as the product of prime factors to determine the LCM
10 = 2 × 5
35 = 5 × 7
LCM (10, 35) = 2 × 5 × 7 = 70
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