LCM of 56 and 70 is 280. The least common multiple denotes the smallest positive integer, which is multiple in a given set of numbers. The LCM concept in the article Least Common Multiple (LCM) is explained in a simple and descriptive manner. If there is any trouble in grasping the LCM concept, students can use this article anytime for free. Let us grasp the method of finding the least common multiple of 56 and 70 using solved examples and FAQs.
What is LCM of 56 and 70?
The Least Common Multiple of 56 and 70 is 280.
How to Find LCM of 56 and 70?
The LCM of 56 and 70 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 56 and 70 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 56 and 70 can be expressed as;
56 = 2 × 2 × 2 × 7
70 = 2 × 5 × 7
LCM (56, 70) = 2 × 2 × 2 × 5 × 7 = 280
LCM of 56 and 70 Using Division Method
In the division method, we divide the numbers 56 and 70 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 56 and 70.
| 2 | 56 | 70 |
| 2 | 28 | 35 |
| 2 | 14 | 35 |
| 5 | 7 | 35 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (56, 70) = 2 × 2 × 2 × 5 × 7 = 280
LCM of 56 and 70 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The below table shows the multiples of 56 and 70.
| Multiples of 56 | Multiples of 70 |
| 56 | 70 |
| 112 | 140 |
| 168 | 210 |
| 224 | 280 |
| 280 | 350 |
| 336 | 420 |
LCM (56, 70) = 280
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 56 and 70?
Solution: 280 is the smallest number that is divisible by both 56 and 70.
2. What is the LCM if the product of two numbers is 3920 and their GCD is 14.
Solution: Given
GCD = 14
Product of numbers = 3920
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 3920 / 14
LCM = 280
Hence the LCM is 280.
Frequently Asked Questions on LCM of 56 and 70
What is the LCM of 56 and 70?
Mention the LCM of 56 and 70 and the HCF of 56 and 70.
What are the methods used to find the LCM of 56 and 70?
The following methods are used to find the LCM of 56 and 70
Prime Factorisation
Division method
Listing of Multiples
Find the GCF if the LCM of 56 and 70 is 280.
GCF × LCM = 56 × 70
Given
LCM = 280
GCF × 280 = 56 × 70
GCF = 14
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