LCM of 25 and 70 is 350. In Mathematics, LCM is divisible exactly by the given numbers. Least common multiples of 25 and 70 can be found if a student knows the common multiples. (25, 50, 75, 100, 125, 150, ….) and (70, 140, 210, 280, 350, 420,….) are the first set of multiples of the numbers 25 and 70. The LCM value can be calculated easily using prime factorisation, the division method and by listing out the multiples.
Also read: Least common multiple
What is LCM of 25 and 70?
The answer to this question is 350. The LCM of 25 and 70 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 25 and 70, is the smallest positive integer 350 which is divisible by both 25 and 70 with no remainder.
How to Find LCM of 25 and 70?
LCM of 25 and 70 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25 and 70 Using Prime Factorisation Method
The prime factorisation of 25 and 70, respectively, is given by:
25 = 5 x 5 = 5²
70 = 2 x 5 x 7 = 2¹ x 5¹ x 7¹
LCM (25, 70) = 350
LCM of 25 and 70 Using Division Method
We’ll divide the numbers (25, 70) by their prime factors to get the LCM of 25 and 70 using the division method (preferably common). The LCM of 25 and 70 is calculated by multiplying these divisors.
|
2 |
25 |
70 |
|
5 |
25 |
35 |
|
5 |
5 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (25, 70) = 350
LCM of 25 and 70 Using Listing the Multiples
To calculate the LCM of 25 and 70 by listing out the common multiples, list the multiples as shown below
- Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, …..
- Multiples of 70 = 70, 140, 210, 280, 350, 420, ……..
LCM (25, 70) = 350
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Video Lesson on Applications of LCM
LCM of 25 and 70 Solved Examples
Question: If the product of two numbers is 1750 and the GCD is 5, find the LCM.
Solution:
It is given that
Product of two numbers = 1750
GCD = 5
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 1750/5
LCM = 350
Hence, the LCM is 350.
Frequently Asked Questions on LCM of 25 and 70
Find the LCM of 25 and 70.
Which methods can be used to get the LCM of 25 and 70?
What is the GCF if the LCM of 25 and 70 is 350?
LCM x GCF = 25 x 70
Given
LCM of 25 and 70 = 350
350 x GCF = 1750
GCF = 1750/350 = 5
What is the LCM of 25 and 70?
Show the relation between GCF and LCM of 25 and 70.
The relation between GCF and LCM of 25 and 70 is
GCF x LCM = 25 x 70
GCF x LCM = 1750
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