LCM of 10 and 60 is 60. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest number among all common multiples of 10 and 60 is the LCM of 10 and 60. (10, 20, 30, 40, 50, etc.) and (60, 120, 180, 240, etc.) are the first few multiples of 10 and 60, respectively. 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 10 and 60?
The answer to this question is 60. The LCM of 10 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 60, is the smallest positive integer 60 which is divisible by both 10 and 60 with no remainder.
How to Find LCM of 10 and 60?
LCM of 10 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 60 Using Prime Factorisation Method
The prime factorisation of 10 and 60, respectively, is given by:
10 = (2 × 5) = 21 × 51 and
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51
LCM (10, 60) = 60
LCM of 10 and 60 Using Division Method
We’ll divide the numbers (10, 60) by their prime factors to get the LCM of 10 and 60 using the division method (preferably common). The LCM of 10 and 60 is calculated by multiplying these divisors.
| 2 | 10 | 60 |
| 2 | 5 | 30 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 60) = 60
LCM of 10 and 60 Using Listing the Multiples
To calculate the LCM of 10 and 60 by listing out the common multiples, list the multiples as shown below
| Multiples of 10 | Multiples of 60 |
| 10 | 60 |
| 20 | 120 |
| 30 | 180 |
| 40 | 240 |
| 50 | 300 |
| 60 | 360 |
The smallest common multiple of 10 and 60 is 60.
Therefore LCM (10, 60) = 60
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LCM of 10 and 60 Solved Example
The GCD and LCM of two numbers are 10 and 60 respectively. If one number is 10, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 10 × p
⇒ p = (GCD × LCM)/10
⇒ p = (10 × 60)/10
⇒ p = 60
Therefore, the other number is 60.
Frequently Asked Questions on LCM of 10 and 60
What is the LCM of 10 and 60?
List the methods used to find the LCM of 10 and 60.
If the LCM of 60 and 10 is 60, Find its GCF.
Since the LCM of 60 and 10 = 60
⇒ 60 × GCF(60, 10) = 600
Therefore, the greatest common factor (GCF) = 600/60 = 10.
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