LCM of 5, 10, 15 and 30 is 30. LCM of 5, 10, 15, and 30 is the smallest number among all common multiples of 5, 10, 15, and 30. The first few multiples of 5, 10, 15, and 30 are (5, 10, 15, 20, 25 . . .), (10, 20, 30, 40, 50 . . .), (15, 30, 45, 60, 75 . . .), and (30, 60, 90, 120, 150 . . .) respectively. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 5, 10, 15 and 30?
The answer to this question is 30. The LCM of 5, 10, 15 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 5, 10, 15 and 30, is the smallest positive integer 30 which is divisible by both 5, 10, 15 and 30 with no remainder.
How to Find LCM of 5, 10, 15 and 30?
LCM of 5, 10, 15 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 10, 15 and 30 Using Prime Factorisation Method
The prime factorisation of 5, 10, 15 and 30, respectively, is given by:
(5) = 51,
10 = (2 × 5) = 21 × 51,
15 = (3 × 5) = 31 × 51, and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (5, 10, 15, 30) = 30
LCM of 5, 10, 15 and 30 Using Division Method
We’ll divide the numbers (5, 10, 15, 30) by their prime factors to get the LCM of 5, 10, 15 and 30 using the division method (preferably common). The LCM of 5, 10, 15 and 30 is calculated by multiplying these divisors.
| 2 | 5 | 10 | 15 | 30 |
| 3 | 5 | 5 | 15 | 15 |
| 5 | 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (5, 10, 15, 30) = 30
LCM of 5, 10, 15 and 30 Using Listing the Multiples
To calculate the LCM of 5, 10, 15 and 30 by listing out the common multiples, list the multiples as shown below
| Multiples of 5 | Multiples of 10 | Multiples of 15 | Multiples of 30 |
| 5 | 10 | 15 | 30 |
| 10 | 20 | 30 | 60 |
| 15 | 30 | 45 | 90 |
| 20 | 40 | 60 | 120 |
| 25 | 50 | 75 | 150 |
| 30 | 60 | 90 | 180 |
The smallest common multiple of 5, 10, 15 and 30 is 30.
Therefore LCM (5, 10, 15, 30) = 30
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LCM of 5, 10, 15 and 30 Solved Example
Question: Find the smallest number that is divisible by 5, 10, 15, 30 exactly.
Solution:
The smallest number that is divisible by 5, 10, 15, and 30 exactly is their LCM.
⇒ Multiples of 5, 10, 15, and 30:
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, . . . .
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, . . . .
Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
Therefore, the LCM of 5, 10, 15, and 30 is 30.
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