LCM of 2, 5 and 7 is 70. We can obtain the least common multiple of 2, 5 and 7 with ease from the common multiples of each number. (2, 4, 6, 8, 10, 12, 14, 16, ….), (5, 10, 15, 20, 25, 30, 35,…..) and (7, 14, 21, 28, 35, 42, ….) are the multiples of 2, 5 and 7. Prime factorisation, division and by listing the multiples are the methods to find the LCM of two numbers.
Also read: Least common multiple
What is LCM of 2, 5 and 7?
The answer to this question is 70. The LCM of 2, 5 and 7 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 2, 5 and 7, is the smallest positive integer 70 which is divisible by both 2, 5 and 7 with no remainder.
How to Find LCM of 2, 5 and 7?
LCM of 2, 5 and 7 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2, 5 and 7 Using Prime Factorisation Method
The prime factorisation of 2, 5 and 7, respectively, is given by:
2 = 2¹
5 = 5¹
7 = 7¹
LCM (2, 5, 7) = 70
LCM of 2, 5 and 7 Using Division Method
We’ll divide the numbers (2, 5, 7) by their prime factors to get the LCM of 2, 5 and 7 using the division method (preferably common). The LCM of 2, 5 and 7 is calculated by multiplying these divisors.
|
2 |
2 |
5 |
7 |
|
5 |
1 |
5 |
7 |
|
7 |
1 |
1 |
7 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (2, 5, 7) = 70
LCM of 2, 5 and 7 Using Listing the Multiples
To calculate the LCM of 2, 5 and 7 by listing out the common multiples, list the multiples as shown below
- Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, . . . ., 66, 68, 70, . . . .
- Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 55, 60, 65, 70, . . . .
- Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 49, 56, 63, 70, . . . .
The smallest common multiple of 2, 5 and 7 is 70.
Therefore, LCM (2, 5, 7) = 70
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
LCM of 2, 5 and 7 Solved Examples
Question: Find the LCM of 2, 5 and 7 in the numbers 40, 50, 25, 70.
Solution:
LCM is the smallest common multiple divisible exactly by the given numbers
The number 70 satisfies this condition
Hence, the LCM is 70.
Frequently Asked Questions on LCM of 2, 5 and 7
How to find the LCM of 2, 5 and 7?
Write the methods to get the LCM of 2, 5 and 7.
If the LCM of 2, 5 and 7 is 70, what is the GCF?
LCM x GCF = 2 x 5 x 7
Given
LCM of 2, 5 and 7 = 70
70 x GCF = 70
GCF = 70/70 = 1
What is the LCM of 2, 5 and 7?
Show the relation between GCF and LCM of 2, 5 and 7.
The relation between GCF and LCM of 2, 5 and 7 is
GCF x LCM = 2 x 5 x 7
GCF x LCM = 70
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