LCM of 80 and 84 is 1680. The smallest number among all common multiples of 80 and 84 is the LCM of 80 and 84. (80, 160, 240, 320, etc.) and (84, 168, 252, 336, 420, 504, etc.) are the first few multiples of 80 and 84, respectively. To find the LCM of 80 and 84, there are three typical methods: prime factorization, division method, and listing multiples. 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 80 and 84?
The answer to this question is 1680. The LCM of 80 and 84 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 80 and 84, is the smallest positive integer 1680 which is divisible by both 80 and 84 with no remainder.
How to Find LCM of 80 and 84?
LCM of 80 and 84 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 80 and 84 Using Prime Factorisation Method
The prime factorisation of 80 and 84, respectively, is given by:
80 = (2 × 2 × 2 × 2 × 5) = 24 × 51 and
84 = (2 × 2 × 3 × 7) = 22 × 31 × 71
LCM (80, 84) = 1680
LCM of 80 and 84 Using Division Method
We’ll divide the numbers (80, 84) by their prime factors to get the LCM of 80 and 84 using the division method (preferably common). The LCM of 80 and 84 is calculated by multiplying these divisors.
| 2 | 80 | 84 |
| 2 | 40 | 42 |
| 2 | 20 | 21 |
| 2 | 10 | 21 |
| 3 | 5 | 21 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (80, 84) = 1680
LCM of 80 and 84 Using Listing the Multiples
To calculate the LCM of 80 and 84 by listing out the common multiples, list the multiples as shown below
| Multiples of 80 | Multiples of 84 |
| 80 | 84 |
| 160 | 168 |
| 240 | 252 |
| ….. | …… |
| 1680 | 1680 |
The smallest common multiple of 80 and 84 is 1680.
Therefore LCM (80, 84) = 1680
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LCM of 80 and 84 Solved Example
The product of two numbers is 6720. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 6720
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 6720/4
Therefore, the LCM is 1680.
The probable combination for the given case is LCM(80, 84) = 1680.
Frequently Asked Questions on LCM of 80 and 84
What is the LCM of 80 and 84?
List the methods used to find the LCM of 80 and 84.
What is the Least Perfect Square Divisible by 80 and 84?
LCM of 80 and 84 = 2 × 2 × 2 × 2 × 3 × 5 × 7 [Incomplete pair(s): 3, 5, 7] ⇒ Least perfect square divisible by each 80 and 84 = LCM(80, 84) × 3 × 5 × 7 = 176400 [Square root of 176400 = √176400 = ±420] Therefore, 176400 is the required number.
If the LCM of 84 and 80 is 1680, Find its GCF.
Since the LCM of 84 and 80 = 1680
⇒ 1680 × GCF(84, 80) = 6720
Therefore, the GCF (greatest common factor) = 6720/1680 = 4.
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