LCM of 7 and 8 is 56. The smallest common multiple of two or more numbers is known as LCM. The article HCF and LCM designed by experts in simple language help students understand the method of finding HCF and LCM of given numbers in a better way. Learn the simple method of finding the least common multiple of 7 and 8 by referring to this article prepared by experts with the aim to provide the best study material for the students.
What is LCM of 7 and 8?
The answer to this question is 56.
How to Find LCM of 7 and 8?
The following methods can be used to determine the LCM of 7 and 8:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7 and 8 Using Prime Factorisation Method
To calculate the least common multiple of 7 and 8 using prime factorisation, we multiply prime factors raised to their respective highest power.
7 = 7
8 = 2 × 2 × 2
LCM (7, 8) = 2 × 2 × 2 × 7 = 56
LCM of 7 and 8 Using Division Method
In division method, we divide the numbers 7 and 8 by their prime factors to find their LCM. The product of these divisors represents the least common multiple of 7 and 8.
|
2 |
7 |
8 |
|
2 |
7 |
4 |
|
2 |
7 |
2 |
|
7 |
7 |
1 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (7, 8) = 2 × 2 × 2 × 7 = 56
LCM of 7 and 8 Using Listing the Multiples
In this method, we list out the multiples of 7 and 8 to find their least common multiple as shown below:
|
Multiples of 7 |
Multiples of 8 |
|
7 |
8 |
|
14 |
16 |
|
21 |
24 |
|
28 |
32 |
|
35 |
40 |
|
42 |
48 |
|
49 |
56 |
|
56 |
64 |
LCM (7, 8) = 56
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Find the LCM if the product of two numbers is 56 and their GCD is 1.
Solution: Given,
GCD = 1
Product of numbers = 56
We know that;
LCM × GCD = Product of numbers
LCM × 1 = 56
LCM = 56
Hence the LCM is 56.
Q. 2: Determine the smallest number that is divisible by 7 and 8 exactly.
Solution: The LCM of 7 and 8 is the smallest number which is divisible by 7 and 8 exactly
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56,….
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56,…….
So, 56 is the smallest number that is divisible by 7 and 8 exactly
Thus the LCM of 7 and 8 is 56.
Frequently Asked Questions on LCM of 7 and 8
What is the LCM of 7 and 8?
Find the GCF if the LCM of 8 and 7 is 56.
LCM (8, 7) + GCF (8, 7) = 8 × 7
Given,
LCM (8, 7) = 56
56 + GCF (8, 7) = 56
GCF (8, 7) = 56/56
GCF (8, 7) = 1
Hence the GCF is 1
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