LCM of 12, 45 and 75 is 900. The common multiple divisible evenly by the given numbers is the LCM. Least common multiple of 12, 45 and 75 is the smallest number we can obtain from the common multiples. (12, 24, 36, 48, 60, ….), (45, 90, 135, 180, 225, ……) and (75, 150, 225, 300, 375,….) are the first few multiples of 12, 45 and 75. Certain methods like division, prime factorisation and listing of multiples can be used to find the LCM.
Also read: Least common multiple
What is LCM of 12, 45 and 75?
The answer to this question is 900. The LCM of 12, 45 and 75 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12, 45 and 75, is the smallest positive integer 900 which is divisible by both 12, 45 and 75 with no remainder.
How to Find LCM of 12, 45 and 75?
LCM of 12, 45 and 75 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 45 and 75 Using Prime Factorisation Method
The prime factorisation of 12, 45 and 75, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
45 = 3 x 3 x 5 = 3² x 5¹
75 = 3 x 5 x 5 = 3¹ x 5²
LCM (12, 45, 75) = 900
LCM of 12, 45 and 75 Using Division Method
We’ll divide the numbers (12, 45, 75) by their prime factors to get the LCM of 12, 45 and 75 using the division method (preferably common). The LCM of 12, 45 and 75 is calculated by multiplying these divisors.
|
2 |
12 |
45 |
75 |
|
2 |
6 |
45 |
75 |
|
3 |
3 |
45 |
75 |
|
3 |
1 |
15 |
25 |
|
5 |
1 |
5 |
25 |
|
5 |
1 |
1 |
5 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (12, 45, 75) = 900
LCM of 12, 45 and 75 Using Listing the Multiples
To calculate the LCM of 12, 45 and 75 by listing out the common multiples, list the multiples as shown below
- Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 864, 876, 888, 900, . . . .
- Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, . . . ., 810, 855, 900, . . .
- Multiples of 75 = 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, . . . ., 675, 750, 825, 900, . . .
LCM (12, 45, 75) = 900
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LCM of 12, 45 and 75 Solved Examples
Question: Which is the LCM of 12, 45 and 75 in 900, 20, 10, 81?
Solution:
LCM of 12, 45 and 75 is the smallest common multiple divisible evenly by the given numbers.
The value which satisfies this condition is 900.
Hence, the LCM is 900.
Frequently Asked Questions on LCM of 12, 45 and 75
Find the LCM of 12, 45 and 75.
What are the methods used to find the LCM of 12, 45 and 75?
Determine the GCF if the LCM of 12, 45 and 75 is 900.
LCM x GCF = 12 x 45 x 75
Given
LCM of 12, 45 and 75 = 900
900 x GCF = 40500
GCF = 40500/900 = 45
What is the LCM of 12, 45 and 75?
Using prime factorisation, find the LCM of 12, 45 and 75.
The LCM value of 12, 45 and 75 using prime factorisation is
12 = 2 x 2 x 3 = 2² x 3¹
45 = 3 x 3 x 5 = 3² x 5¹
75 = 3 x 5 x 5 = 3¹ x 5²
Therefore, the LCM is 900.
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