LCM of 5, 8 and 10 is 40. The smallest number among all frequent multiples of 5, 8, and 10 is the LCM of 5, 8, and 10. The first few multiples of 5, 8, and 10 are (5, 10, 15, 20, 25, etc. ), (8, 16, 24, 32, 40, etc.) and (10, 20, 30, 40, 50, etc.). The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. 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, 8 and 10?
The answer to this question is 40. The LCM of 5, 8 and 10 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 5, 8 and 10, is the smallest positive integer 40 which is divisible by both 5, 8 and 10 with no remainder.
How to Find LCM of 5, 8 and 10?
LCM of 5, 8 and 10 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 8 and 10 Using Prime Factorisation Method
The prime factorisation of 5, 8 and 10, respectively, is given by:
(5) = 51,
8 = (2 × 2 × 2) = 23, and
10 = (2 × 5) = 21 × 51
LCM (5, 8, 10) = 40
LCM of 5, 8 and 10 Using Division Method
We’ll divide the numbers (5, 8, 10) by their prime factors to get the LCM of 5, 8 and 10 using the division method (preferably common). The LCM of 5, 8 and 10 is calculated by multiplying these divisors.
| 2 | 5 | 8 | 10 |
| 2 | 5 | 4 | 5 |
| 5 | 5 | 2 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (5, 8, 10) = 40
LCM of 5, 8 and 10 Using Listing the Multiples
To calculate the LCM of 5, 8 and 10 by listing out the common multiples, list the multiples as shown below
| Multiples of 5 | Multiples of 8 | Multiples of 10 |
| 5 | 8 | 10 |
| 10 | 16 | 20 |
| 15 | 24 | 30 |
| 20 | 32 | 40 |
| 25 | 40 | 50 |
| 30 | 48 | 60 |
| 35 | 56 | 70 |
| 40 | 64 | 80 |
The smallest common multiple of 5, 8 and 10 is 72.
Therefore LCM (5, 8, 10) = 40
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LCM of 5, 8 and 10 Solved Example
Verify the relationship between the GCD and LCM of 5, 8, and 10.
Solution:
The relation between GCD and LCM of 5, 8, and 10 is given as,
LCM(5, 8, 10) = [(5 × 8 × 10) × GCD(5, 8, 10)]/[GCD(5, 8) × GCD(8, 10) × GCD(5, 10)]
Prime factorization of 5, 8 and 10:
5 = 5
8 = 23
10 = 2 × 5
∴ GCD of (5, 8), (8, 10), (5, 10) and (5, 8, 10) = 1, 2, 5 and 1 respectively.
Now, LHS = LCM(5, 8, 10) = 40.
And, RHS = [(5 × 8 × 10) × GCD(5, 8, 10)]/[GCD(5, 8) × GCD(8, 10) × GCD(5, 10)] = [(400) × 1]/[1 × 2 × 5] = 40
LHS = RHS = 40.
Hence verified.
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