LCM of 10, 15 and 25 is 150. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. Experts formulated the article Least Common Multiple (LCM) in a simple language to help students solve the problems in a shorter duration with a clear idea of the LCM concept. Practising the problems using this article enable students to improve their skills which are vital for a better academic score. Here, we will learn how to find the least common multiple of 10, 15 and 25 in a detailed manner.
What is LCM of 10, 15 and 25?
The Least Common Multiple of 10, 15 and 25 is 150.
How to Find LCM of 10, 15 and 25?
The LCM of 10, 15 and 25 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 10, 15 and 25 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 10, 15 and 25 can be expressed as;
10 = 2 × 5
15 = 3 × 5
25 = 5 × 5
LCM (10, 15, 25) = 2 × 3 × 5 × 5 = 150
LCM of 10, 15 and 25 Using Division Method
In the division method, we divide the numbers 10, 15 and 25 by a common prime number until the remainder is a prime number or one. The product of these divisors shows the least common multiple of 10, 15 and 25.
| 2 | 10 | 15 | 25 |
| 3 | 5 | 15 | 25 |
| 5 | 5 | 5 | 25 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (10, 15, 25) = 2 × 3 × 5 × 5 = 150
LCM of 10, 15 and 25 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The below table shows the multiples of 10, 15 and 25.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, …….., 130, 140, 150, ……….
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, …………
Multiples of 25: 25, 50, 75, 100, 125, 150, ………….
LCM (10, 15, 25) = 150
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 10,15, 25 exactly?
Solution: The smallest number that is divisible by 10, 15, 25 exactly is their LCM. The LCM of 10, 15, 25 is 150. Hence the smallest number that is divisible by 10, 15, 25 exactly is 150.
Frequently Asked Questions on LCM of 10, 15 and 25
What is the LCM of 10, 15 and 25?
Write the LCM of 10, 15 and 25 and the HCF of 10, 15 and 25.
Is 150 the LCM of 10, 15 and 25?
Mention the methods used to determine the LCM of 10, 15 and 25.
The following methods are used to determine the LCM of 10, 15 and 25
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 10, 15 and 25 by prime factorisation method.
In this method, the given numbers are expressed as the product of prime factors to find the LCM
10 = 2 × 5
15 = 3 × 5
25 = 5 × 5
LCM (10, 15, 25) = 2 × 3 × 5 × 5 = 150
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