LCM of 60 and 100 is 300. The smallest number among all common multiples of 60 and 100 is the LCM of 60 and 100. (60, 120, 180, 240, etc.) and (100, 200, 300, 400, 500, 600, 700, etc.) are the first few multiples of 60 and 100, respectively. To find the LCM of 60 and 100, there are three main methods: division, listing multiples, and prime factorization. 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 100?
The answer to this question is 300. The LCM of 60 and 100 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 60 and 100, is the smallest positive integer 300 which is divisible by both 60 and 100 with no remainder.
How to Find LCM of 60 and 100?
LCM of 60 and 100 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 100 Using Prime Factorisation Method
The prime factorisation of 60 and 100, respectively, is given by:
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51 and
100 = (2 × 2 × 5 × 5) = 22 × 52
LCM (60, 100) = 300
LCM of 60 and 100 Using Division Method
We’ll divide the numbers (60, 100) by their prime factors to get the LCM of 60 and 100 using the division method (preferably common). The LCM of 60 and 100 is calculated by multiplying these divisors.
| 2 | 60 | 100 |
| 2 | 30 | 50 |
| 3 | 15 | 25 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (60, 100) = 300
LCM of 60 and 100 Using Listing the Multiples
To calculate the LCM of 60 and 100 by listing out the common multiples, list the multiples as shown below
| Multiples of 60 | Multiples of 100 |
| 60 | 100 |
| 120 | 200 |
| 180 | 300 |
| 240 | 400 |
| 300 | 500 |
The smallest common multiple of 60 and 100 is 300.
Therefore LCM (60, 100) = 300
Related Articles
Video Lesson on Applications of LCM
LCM of 60 and 100 Solved Example
Questin: Find the smallest number that is divisible by 60 and 100 exactly.
Solution:
The smallest number that is divisible by 60 and 100 exactly is their LCM.
⇒ Multiples of 60 and 100:
Multiples of 60 = 60, 120, 180, 240, 300, . . . .
Multiples of 100 = 100, 200, 300, 400, 500, . . . .
Therefore, the LCM of 60 and 100 is 300.
Frequently Asked Questions on LCM of 60 and 100
What is the LCM of 60 and 100?
List the methods used to find the LCM of 60 and 100.
If the LCM of 100 and 60 is 300, Find its GCF.
Since the LCM of 100 and 60 = 300
⇒ 300 × GCF(100, 60) = 6000
Therefore, the greatest common factor (GCF) = 6000/300 = 20.
Which of the following is the LCM of 60 and 100? 300, 12, 11, 30
What is the Least Perfect Square Divisible by 60 and 100?
LCM of 60 and 100 = 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 3] ⇒ Least perfect square divisible by each 60 and 100 = LCM(60, 100) × 3 = 900 [Square root of 900 = √900 = ±30] Therefore, 900 is the required number.
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