LCM of 10, 25, 35 and 40 is 1400. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Least common multiple of 10, 25, 35, and 40 is the smallest number among all common multiples of 10, 25, 35, and 40. The first few multiples of 10, 25, 35, and 40 are (10, 20, 30, 40, 50 . . .), (25, 50, 75, 100, 125 . . .), (35, 70, 105, 140, 175 . . .), and (40, 80, 120, 160, 200 . . .) respectively. 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 10, 25, 35 and 40?
The answer to this question is 1400. The LCM of 10, 25, 35 and 40 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10, 25, 35 and 40, is the smallest positive integer 1400 which is divisible by both 10, 25, 35 and 40 with no remainder.
How to Find LCM of 10, 25, 35 and 40?
LCM of 10, 25, 35 and 40 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10, 25, 35 and 40 Using Prime Factorisation Method
The prime factorisation of 10, 25, 35 and 40, respectively, is given by:
10 = (2 × 5) = 21 × 51,
25 = (5 × 5) = 52,
35 = (5 × 7) = 51 × 71, and
40 = (2 × 2 × 2 × 5) = 23 × 51
LCM (10, 25, 35, 40) = 1400
LCM of 10, 25, 35 and 40 Using Division Method
We’ll divide the numbers (10, 25, 35, 40) by their prime factors to get the LCM of 10, 25, 35 and 40 using the division method (preferably common). The LCM of 10, 25, 35 and 40 is calculated by multiplying these divisors.
| 2 | 10 | 25 | 35 | 40 |
| 2 | 5 | 25 | 35 | 20 |
| 5 | 5 | 25 | 35 | 10 |
| 2 | 1 | 5 | 7 | 2 |
| 5 | 1 | 5 | 7 | 1 |
| 7 | 1 | 1 | 7 | 1 |
| x | 1 | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (10, 25, 35, 40) = 1400
LCM of 10, 25, 35 and 40 Using Listing the Multiples
To calculate the LCM of 10, 25, 35 and 40 by listing out the common multiples, list the multiples as shown below
| Multiples of 10 | Multiples of 25 | Multiples of 35 | Multiples of 40 |
| 10 | 25 | 35 | 40 |
| 20 | 50 | 75 | 80 |
| 30 | 75 | 105 | 120 |
| …… | …. | …… | …… |
| 1400 | 1400 | 1400 | 1400 |
The smallest common multiple of 10, 25, 35 and 40 is 1400.
Therefore LCM (10, 25, 35, 40) = 1400
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LCM of 10, 25, 35 and 40 Solved Example
Question: Find the smallest number that is divisible by 10, 25, 35, 40 exactly.
Solution:
The value of LCM(10, 25, 35, 40) will be the smallest number that is exactly divisible by 10, 25, 35, and 40.
⇒ Multiples of 10, 25, 35, and 40:
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 1360, 1370, 1380, 1390, 1400, . . . .
Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 1300, 1325, 1350, 1375, 1400, . . . .
Multiples of 35 = 35, 70, 105, 140, 175, 210, 245, 280, 315, 350, . . . ., 1260, 1295, 1330, 1365, 1400, . . . .
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 1320, 1360, 1400, . . . .
Therefore, the LCM of 10, 25, 35, and 40 is 1400.
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