LCM of 60 and 72 is 360. Among all common multiples of 60 and 72, the LCM of 60 and 72 is the smallest. (60, 120, 180, 240, 300, 360,…) and (72, 144, 216, 288, 360,…) are the first few multiples of 60 and 72, respectively. To find the LCM of 60 and 72, you can use one of three methods: listing multiples, prime factorization, or division. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
What is LCM of 60 and 72?
The answer to this question is 360. The LCM of 60 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 60 and 72, is the smallest positive integer 360 which is divisible by both 60 and 72 with no remainder.
Also read: Least common multiple
How to Find LCM of 60 and 72?
LCM of 60 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 72 Using Prime Factorisation Method
The prime factorisation of 60 and 72, respectively, is given by:
(2 × 2 × 3 × 5) = 22 × 31 × 51 and (2 × 2 × 2 × 3 × 3) = 23 × 32
LCM (60, 72) = 360
LCM of 60 and 72 Using Division Method
We’ll divide the numbers (60, 72) by their prime factors to get the LCM of 60 and 72 using the division method (preferably common). The LCM of 60 and 72 is calculated by multiplying these divisors.
| 2 | 60 | 72 |
| 2 | 30 | 36 |
| 2 | 15 | 18 |
| 2 | 15 | 9 |
| 3 | 5 | 3 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (60, 72) = 360
LCM of 60 and 72 Using Listing the Multiples
To calculate the LCM of 60 and 72 by listing out the common multiples, list the multiples as shown below.
| Multiples of 60 | Multiples of 72 |
| 60 | 72 |
| 120 | 144 |
| 180 | 216 |
| 240 | 288 |
| 300 | 360 |
| 360 | 432 |
The smallest common multiple of 60 and 72 is 360.
LCM (60, 72) = 360
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LCM of 60 and 72 Solved Example
Question: The product of two numbers is 4320. If their GCD is 12, what is their LCM?
1
Solution:
Given: GCD = 12
product of numbers = 4320
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 4320/12
Therefore, the LCM is 360.
The probable combination for the given case is LCM(60, 72) = 360.
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