LCM of 63, 70 and 77 is 6930. LCM is the method which is used to find the smallest common multiple between the numbers 63, 70 and 77. Least common multiples of 63, 70 and 77 can be determined by analyzing the common multiples of the numbers. (63, 126, 189, 252, 315, ….), (70, 140, 210, 280, 350, …..) and (77, 154, 231, 308, 385, ….) are the multiples of 63, 70 and 77. The LCM of two numbers is calculated by listing the multiples, prime factorization method and division method.
Also read: Least common multiple
What is LCM of 63, 70 and 77?
The answer to this question is 6930. The LCM of 63, 70 and 77 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 63, 70 and 77, is the smallest positive integer 6930 which is divisible by both 63, 70 and 77 with no remainder.
How to Find LCM of 63, 70 and 77?
LCM of 63, 70 and 77 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 63, 70 and 77 Using Prime Factorisation Method
The prime factorisation of 63, 70 and 77, respectively, is given by:
63 = 3 x 3 x 7 = 3² x 7¹
70 = 2¹ x 5¹ x 7¹
77 = 7¹ x 11¹
LCM (63, 70, 77) = 6930
LCM of 63, 70 and 77 Using Division Method
We’ll divide the numbers (63, 70, 77) by their prime factors to get the LCM of 63, 70 and 77 using the division method (preferably common). The LCM of 63, 70 and 77 is calculated by multiplying these divisors.
2 |
63 |
70 |
77 |
3 |
63 |
35 |
77 |
3 |
21 |
35 |
77 |
5 |
7 |
35 |
77 |
7 |
7 |
7 |
77 |
11 |
1 |
1 |
11 |
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (63, 70, 77) = 6930
LCM of 63, 70 and 77 Using Listing the Multiples
To calculate the LCM of 63, 70 and 77 by listing out the common multiples, list the multiples as shown below
Multiples of 63 = 63, 126, 189, 252, 315, …..
Multiples of 70 = 70, 140, 210, 280, 350, 420, ….
Multiples of 77 = 77, 154, 231, 308, 385, ….
LCM (63, 70, 77) = 6930
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
![](https://cdn1.byjus.com/wp-content/uploads/2022/04/Application-of-LCM.jpg)
LCM of 63, 70 and 77 Solved Examples
Question: Determine the smallest number which is exactly divisible by 63, 70 and 77.
Solution:
We know that
LCM is the smallest number exactly divisible by 63, 70 and 77.
Multiples of 63 = 63, 126, 189, 252, 315, 378, 441, 504, 567, 630, . . . ., 6741, 6804, 6867, 6930, . . . .
Multiples of 70 = 70, 140, 210, 280, 350, 420, 490, 560, 630, 700, . . . ., 6720, 6790, 6860, 6930, . . . .
Multiples of 77 = 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, . . . ., 6699, 6776, 6853, 6930, . . . .
Hence, the LCM of 63, 70 and 77 is 6930.
Frequently Asked Questions on LCM of 63, 70 and 77
What methods can we use to find the LCM of 63, 70 and 77?
The methods which we can use to find the LCM of 63, 70 and 77 are
Prime Factorisation
Division method
Listing the multiples
By using prime factorisation, determine the LCM of 63, 70 and 77.
To find the LCM, the factors must be known
63 = 3 x 3 x 7 = 3² x 7¹
70 = 2¹ x 5¹ x 7¹
77 = 7¹ x 11¹
LCM is the product of prime factors raised to the highest exponent among 63, 70 and 77.
LCM of 63, 70, 77 = 6930
Find the GCF if the LCM of 63, 70 and 77 is 6930.
LCM x GCF = 63 x 70 x 77
As the LCM = 6930
6930 x GCF = 339570
GCF = 339570/6930 = 49
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