LCM of 7 and 56 is 56. The value which is evenly divisible by the numbers 7 and 56 is the LCM value. The least common multiple of 7 and 56 can be calculated effortlessly by using the common multiples. The multiples of 7 are (7, 14, 21, 28, 35, ….) and the multiples of 56 are (56, 112, 168, 224, ….) respectively. The methods used to determine the LCM of 7 and 56 are prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 7 and 56?
The answer to this question is 56. The LCM of 7 and 56 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 7 and 56, is the smallest positive integer 56 which is divisible by both 7 and 56 with no remainder.
How to Find LCM of 7 and 56?
LCM of 7 and 56 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7 and 56 Using Prime Factorisation Method
The prime factorisation of 7 and 56, respectively, is given by:
7 = 7 = 7¹
56 = 2 x 2 x 2 x 7 = 2³ x 7¹
LCM (7, 56) = 56
LCM of 7 and 56 Using Division Method
We’ll divide the numbers (7, 56) by their prime factors to get the LCM of 7 and 56 using the division method (preferably common). The LCM of 7 and 56 is calculated by multiplying these divisors.
|
2 |
7 |
56 |
|
2 |
7 |
28 |
|
2 |
7 |
14 |
|
7 |
7 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (7, 56) = 56
LCM of 7 and 56 Using Listing the Multiples
To calculate the LCM of 7 and 56 by listing out the common multiples, list the multiples as shown below
|
Multiples of 7 |
Multiples of 56 |
|
7 |
56 |
|
14 |
112 |
|
21 |
168 |
|
28 |
224 |
|
35 |
280 |
|
42 |
336 |
|
49 |
392 |
|
56 |
448 |
LCM (7, 56) = 56
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Video Lesson on Applications of LCM
LCM of 7 and 56 Solved Examples
Question: The LCM and GCD of two numbers are 56 and 7 respectively. If one number is 7, what is the other number?
Solution:
Consider the number as z
We know that
GCD x LCM = 7 x z
z = (GCD x LCM)/7
Substituting the values
z = (7 x 56)/7
z = 56
Hence, the other number is 56.
Frequently Asked Questions on LCM of 7 and 56
Calculate the GCF, if the LCM of 7 and 56 is 56.
We know that
LCM x GCF = 7 x 56
As LCM (7, 56) is 56
56 x GCF = 7 x 56
GCF = (7 x 56)/56 = 7
Determine the LCM of 7 and 56.
To find the LCM, the multiples of 7 and 56 has to be obtained
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, ….
Multiples of 56 = 56, 112, 168, 224, 280, 336, 392, ….
The smallest multiple exactly divisible by 7 and 56 is 56.
Write the relation between GCF and LCM of 7 and 56.
The relation between GCF and LCM of 7 and 56 is
LCM x GCF = 7 x 56
LCM x GCF = 392
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