LCM of 3, 5 and 10 is 30. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 3, 5, and 10, LCM of 3, 5, and 10 is the smallest number. (3, 6, 9, 12, 15, etc. ), (5, 10, 15, 20, 25, etc. ), and (10, 20, 30, 40, 50, etc.) are the first few multiples of 3, 5, and 10. Listing multiples, division method, and prime factorization are three common methods for determining the LCM of 3, 5, and 10.
Also read: Least common multiple
What is LCM of 3, 5 and 10?
The answer to this question is 30. The LCM of 3, 5 and 10 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3, 5 and 10, is the smallest positive integer 30 which is divisible by both 3, 5 and 10 with no remainder.
How to Find LCM of 3, 5 and 10?
LCM of 3, 5 and 10 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 5 and 10 Using Prime Factorisation Method
The prime factorisation of 3, 5 and 10, respectively, is given by:
(3) = 31,
(5) = 51, and
(2 × 5) = 21 × 51
LCM (3, 5, 10) = 30
LCM of 3, 5 and 10 Using Division Method
We’ll divide the numbers (3, 5, 10) by their prime factors to get the LCM of 3, 5 and 10 using the division method (preferably common). The LCM of 3, 5 and 10 is calculated by multiplying these divisors.
| 2 | 3 | 5 | 10 |
| 3 | 3 | 5 | 5 |
| 5 | 1 | 5 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (3, 5, 10) = 30
LCM of 3, 5 and 10 Using Listing the Multiples
To calculate the LCM of 3, 5 and 10 by listing out the common multiples, list the multiples as shown below
| Multiples of 3 | Multiples of 5 | Multiples of 10 |
| 3 | 5 | 10 |
| 6 | 10 | 20 |
| 9 | 15 | 30 |
| 12 | 20 | 40 |
| … | 25 | 50 |
| 30 | 30 | 60 |
The smallest common multiple of 3, 5 and 10 is 30.
Therefore LCM (3, 5, 10) = 30
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LCM of 3, 5 and 10 Solved Example
Find the smallest number that is divisible by 3, 5, 10 exactly.
Solution:
The smallest number that is divisible by 3, 5, and 10 exactly is their LCM.
⇒ Multiples of 3, 5, and 10:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . .
Multiples of 5 = 5, 10, 15, 20, 25, 30, . . . .
Multiples of 10 = 10, 20, 30, 40, 50, . . . .
Therefore, the LCM of 3, 5, and 10 is 30.
Frequently Asked Questions on LCM of 3, 5 and 10
What is the LCM of 3, 5 and 10?
List the methods used to find the LCM of 3, 5 and 10.
What is the Relation Between GCF and LCM of 3, 5, 10?
What is the Least Perfect Square Divisible by 3, 5, and 10?
LCM of 3, 5, and 10 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 3, 5, and 10 = LCM(3, 5, 10) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30] Therefore, 900 is the required number.
How to Find the LCM of 3, 5, and 10 by Prime Factorization?
⇒ LCM of 3, 5, 10 = 2 × 3 × 5 = 30.
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