LCM of 80, 85 and 90 is 12240. The evenly divisible number which is the smallest among the multiples provides the value of LCM. By listing down the multiples, easily we can find the least common multiple of 80, 85 and 90. (80, 160, 240, 320, 400, 480, ….), (85, 170, 255, 340, 425, ….) and (90, 180, 270, 360, 450,….) are the multiples of 80, 85 and 90. You can find the LCM of 80, 85 and 90 using the prime factorisation method, division method and by listing out the multiples.
Also read: Least common multiple
What is LCM of 80, 85 and 90?
The answer to this question is 12240. The LCM of 80, 85 and 90 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 80, 85 and 90, is the smallest positive integer 12240 which is divisible by both 80, 85 and 90 with no remainder.
How to Find LCM of 80, 85 and 90?
LCM of 80, 85 and 90 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 80, 85 and 90 Using Prime Factorisation Method
The prime factorisation of 80, 85 and 90, respectively, is given by:
80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5¹
85 = 5 x 17 = 5¹ x 17¹
90 = 2 x 3 x 3 x 5 = 2¹ x 3² x 5¹
LCM (80, 85, 90) = 12240
LCM of 80, 85 and 90 Using Division Method
We’ll divide the numbers (80, 85, 90) by their prime factors to get the LCM of 80, 85 and 90 using the division method (preferably common). The LCM of 80, 85 and 90 is calculated by multiplying these divisors.
|
2 |
80 |
85 |
90 |
|
2 |
40 |
85 |
45 |
|
2 |
20 |
85 |
45 |
|
2 |
10 |
85 |
45 |
|
3 |
5 |
85 |
45 |
|
3 |
5 |
85 |
15 |
|
5 |
5 |
85 |
5 |
|
17 |
1 |
17 |
1 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (80, 85, 90) = 12240
LCM of 80, 85 and 90 Using Listing the Multiples
To calculate the LCM of 80, 85 and 90 by listing out the common multiples, list the multiples as shown below
Multiples of 80 = 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, . . . ., 12080, 12160, 12240, . . . .
Multiples of 85 = 85, 170, 255, 340, 425, 510, 595, 680, 765, 850, . . . ., 12070, 12155, 12240, . . . .
Multiples of 90 = 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, . . . ., 11970, 12060, 12150, 12240, . . . .
LCM (80, 85, 90) = 12240
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LCM of 80, 85 and 90 Solved Examples
Question: Find the LCM of 80, 85 and 90 among the following numbers. 3, 10, 12240, 36
Solution:
The LCM value is the smallest common multiple of 80, 85 and 90
The number which satisfies this condition is 12240
Hence, the LCM is 12240.
Frequently Asked Questions on LCM of 80, 85 and 90
What is the LCM of 80, 85 and 90?
List the methods used to get the LCM of 80, 85 and 90
Using the prime factorisation method, calculate the LCM of 80, 85 and 90.
Using the prime factorisation method
80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5¹
85 = 5 x 17 = 5¹ x 17¹
90 = 2 x 3 x 3 x 5 = 2¹ x 3² x 5¹
Therefore, the LCM is 12240.
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