LCM of 60 and 66 is 660. Among all common multiples of 60 and 66, the LCM of 60 and 66 is the smallest number. (60, 120, 180, 240, 300,…) and (66, 132, 198, 264,…) are the first few multiples of 60 and 66, respectively. The division technique, prime factorization, and listing multiples are the three most frequent ways for finding the LCM of 60 and 66. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 60 and 66?
The answer to this question is 660. The LCM of 60 and 66 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 60 and 66, is the smallest positive integer 660 which is divisible by both 60 and 66 with no remainder.
How to Find LCM of 60 and 66?
LCM of 60 and 66 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 66 Using Prime Factorisation Method
The prime factorisation of 60 and 66, respectively, is given by:
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51 and
66 = (2 × 3 × 11) = 21 × 31 × 111
LCM (60, 66) = 660
LCM of 60 and 66 Using Division Method
We’ll divide the numbers (60, 66) by their prime factors to get the LCM of 60 and 66 using the division method (preferably common). The LCM of 60 and 66 is calculated by multiplying these divisors.
| 2 | 60 | 66 |
| 2 | 30 | 33 |
| 3 | 15 | 33 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (60, 66) = 660
LCM of 60 and 66 Using Listing the Multiples
To calculate the LCM of 60 and 66 by listing out the common multiples, list the multiples as shown below.
| Multiples of 60 | Multiples of 66 |
| 60 | 66 |
| 120 | 132 |
| 180 | 198 |
| …. | …. |
| 660 | 660 |
The smallest common multiple of 60 and 66 is 660.
Therefore LCM (60, 66) = 660
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LCM of 60 and 66 Solved Example
The GCD and LCM of two numbers are 6 and 660 respectively. If one number is 60, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 60 × b
⇒ b = (GCD × LCM)/60
⇒ b = (6 × 660)/60
⇒ b = 66
Therefore, the other number is 66.
Frequently Asked Questions on LCM of 60 and 66
What is the LCM of 60 and 66?
List the methods used to find the LCM of 60 and 66.
If the LCM of 66 and 60 is 660, Find its GCF.
Since the LCM of 66 and 60 = 660
⇒ 660 × GCF(66, 60) = 3960
Therefore, the GCF (greatest common factor) = 3960/660 = 6.
What is the Least Perfect Square Divisible by 60 and 66?
LCM of 60 and 66 = 2 × 2 × 3 × 5 × 11 [Incomplete pair(s): 3, 5, 11] ⇒ Least perfect square divisible by each 60 and 66 = LCM(60, 66) × 3 × 5 × 11 = 108900 [Square root of 108900 = √108900 = ±330] Therefore, 108900 is the required number.
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