LCM of 10 and 95 is 190. Students will understand the concept of least common multiples of 10 and 95 using the common multiples. (10, 20, 30, 40, 50, 60, 70, ….) and (95, 190, 285, 380, 475,….) are the multiples of 10 and 95. The LCM of two numbers as per the prime factorization, division and by listing the multiples methods are given in a stepwise format here to help students ace well in their exams.
Also read: Least common multiple
What is LCM of 10 and 95?
The answer to this question is 190. The LCM of 10 and 95 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 95, is the smallest positive integer 190 which is divisible by both 10 and 95 with no remainder.
How to Find LCM of 10 and 95?
LCM of 10 and 95 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 95 Using Prime Factorisation Method
The prime factorisation of 10 and 95, respectively, is given by:
10 = 2 x 5 = 2¹ x 5¹
95 = 5 x 19 = 5¹ x 19¹
LCM (10, 95) = 190
LCM of 10 and 95 Using Division Method
We’ll divide the numbers (10, 95) by their prime factors to get the LCM of 10 and 95 using the division method (preferably common). The LCM of 10 and 95 is calculated by multiplying these divisors.
|
2 |
10 |
95 |
|
5 |
5 |
95 |
|
19 |
1 |
19 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (10, 95) = 190
LCM of 10 and 95 Using Listing the Multiples
To calculate the LCM of 10 and 95 by listing out the common multiples, list the multiples as shown below.
Multiples of 10 = 10, 20, 30, 40, 50, 60, ……., 160, 170, 180, 190, ……
Multiples of 95 = 95, 190, 285, 380, 475, ………
LCM (10, 95) = 190
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 10 and 95 Solved Examples
Question: The LCM and GCD of two numbers are 190 and 5. If one of the numbers is 95, determine the other.
Solution:
Given
LCM = 190
GCD = 5
Consider z as the other number
GCD x LCM = 95 x z
5 x 190 = 95 x z
z = (5 x 190)/95
z = 10
Hence, the LCM of 10 and 95 is 10.
Frequently Asked Questions on LCM of 10 and 95
What is the LCM of 10 and 95 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
10 = 2 x 5 = 2¹ x 5¹
95 = 5 x 19 = 5¹ x 19¹
LCM of 10 and 95 is the product of prime factors raised to the highest exponent among the numbers 10 and 95
LCM of 10 and 95 = 190
If the LCM of 10 and 95 is 190, find the GCF.
LCM x GCF = 10 x 95
Given
LCM of 10 and 95 = 190
190 x GCF = 950
GCF = 950/190 = 5
Show the relation between GCF and LCM of 10 and 95.
The relation between GCF and LCM of 10 and 95 is
LCM x GCF = 25 x 75
LCM x GCF = 1875
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