LCM of 60 and 75 is 300. The division technique, prime factorization, and listing multiples are the three most frequent ways for finding the LCM of 60 and 75. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 60 and 75?
The answer to this question is 300. The LCM of 60 and 75 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 60 and 75, is the smallest positive integer 300 which is divisible by both 60 and 75 with no remainder.
How to Find LCM of 60 and 75?
LCM of 60 and 75 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 75 Using Prime Factorisation Method
The prime factorisation of 60 and 75, respectively, is given by:
60 = 2 × 2 × 3 × 5 and
75 = 3 × 5 × 5
LCM (60, 75) = 300
LCM of 60 and 75 Using Division Method
We’ll divide the numbers (60, 75) by their prime factors to get the LCM of 60 and 75 using the division method (preferably common). The LCM of 60 and 75 is calculated by multiplying these divisors.
|
3 |
60 |
75 |
|
5 |
20 |
25 |
|
5 |
4 |
5 |
|
2 |
4 |
1 |
|
2 |
2 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (60, 75) = 300
LCM of 60 and 75 Using Listing the Multiples
To calculate the LCM of 60 and 75 by listing out the common multiples, list the multiples as shown below
|
Multiples of 60 |
Multiples of 75 |
|
60 |
75 |
|
120 |
150 |
|
180 |
225 |
|
240 |
300 |
|
300 |
375 |
|
360 |
– |
|
420 |
– |
The smallest common multiple of 60 and 75 is 300.
LCM (60, 75) = 300
Related Articles
Video Lesson on Applications of LCM
LCM of 60 and 75 Solved Example
Find the smallest number that is divisible by 60 and 75 exactly.
The smallest number that is divisible by 60 and 75 exactly is their LCM.
Multiples of 60 and 75:
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, . . . .
Multiples of 75 =75, 150, 225, 300, . . . .
Therefore, the LCM of 60 and 75 is 300.
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