LCM of 45, 60 and 75 is 900. The Lowest/Least Common Multiple commonly known as LCM, is the smallest number that is divisible by the given set of numbers. In the given set of numbers 45, 60 and 75, 900 is the first(least or smallest) number that is common in the set of multiples of 45, 60 and 75. The LCM, also referred to as LCD, Least Common Divisor for 45, 60 and 75 is 900. You can use the Prime Factorization and Division method to find the LCM for any given set of numbers.
What is LCM of 45, 60 and 75
The Least Common Multiple or Lowest Common Multiple of 45, 60 and 75 is 900.
How to Find LCM of 45, 60 and 75?
LCM of 45, 60 and 75 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 45, 60 and 75 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 45, 60 and 75 can be expressed as;
45 = 3 × 3 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
3 × 5 is the common prime factor of 45, 60 and 75. This is multiplied by the other prime factors to get the LCM.
LCM (45, 60, 75) = 2 × 2 × 3 × 3 × 5 × 5 = 900
LCM of 45, 60 and 75 Using Division Method
In the Division Method, the following steps are done
- Divide 45, 60 and 75 together with a smallest common prime divisor
- When there are no common divisors, divide with prime factors till the remainders are 1 for all 3.
- Multiply the prime divisors to get the LCM
|
2 |
45 |
60 |
75 |
|
2 |
45 |
30 |
75 |
|
3 |
45 |
15 |
75 |
|
3 |
15 |
5 |
25 |
|
5 |
5 |
5 |
25 |
|
5 |
1 |
1 |
5 |
|
× |
1 |
1 |
1 |
LCM (45, 60, 75) = 2 × 2 × 3 × 3 × 5 × 5 = 900
LCM of 45, 60 and 75 Using Listing the Multiples
By listing all the multiples of 45, 60 and 75, we can identify the least common multiple, which is the LCM. Below is the list of multiples for 45, 60 and 75
Multiples of 45
45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990
Multiples of 60
60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020
Multiples of 75
75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, 900, 975, 1050
LCM (45, 60, 75) = 900
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 45, 60 and 75?
Answer: 900 is the smallest number that is divisible by 45, 60 and 75.
What is the LCM for 5, 10, 45, 60 and 75?
Answer: LCM for 5, 10, 45, 60 and 75 is 900 as 5 is a prime factor of 45, 60, 75 and 10 is the factor of 60.
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