LCM of 21 and 30 is 210. Among all common multiples of 21 and 30, the LCM of 21 and 30 is the smallest number. (21, 42, 63, 84, 105, and so on) and (30, 60, 90, 120, and so on) are the first few multiples of 21 and 30. The division method, listing multiples, and prime factorization are the three most prevalent methods for calculating the LCM of 21 and 30. 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 21 and 30?
The answer to this question is 210. The LCM of 21 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 21 and 30, is the smallest positive integer 210 which is divisible by both 21 and 30 with no remainder.
How to Find LCM of 21 and 30?
LCM of 21 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 30 Using Prime Factorisation Method
The prime factorisation of 21 and 30, respectively, is given by:
21 = (3 × 7) = 31 × 71 and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (21, 30) = 210
LCM of 21 and 30 Using Division Method
We’ll divide the numbers (21, 30) by their prime factors to get the LCM of 21 and 30 using the division method (preferably common). The LCM of 21 and 30 is calculated by multiplying these divisors.
| 2 | 21 | 30 |
| 3 | 21 | 15 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (21, 30) = 210
LCM of 21 and 30 Using Listing the Multiples
To calculate the LCM of 21 and 30 by listing out the common multiples, list the multiples as shown below.
| Multiples of 21 | Multiples of 30 |
| 21 | 30 |
| 42 | 60 |
| 63 | 90 |
| …. | ……. |
| 210 | 210 |
The smallest common multiple of 21 and 30 is 210.
Therefore LCM (21, 30) = 210
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Video Lesson on Applications of LCM
LCM of 21 and 30 Solved Example
Question: Find the smallest number that is divisible by 21 and 30 exactly.
Solution:
Their LCM is the smallest number that is exactly divisible by 21 and 30.
⇒ Multiples of 21 and 30:
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . .
Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
As a result, the LCM of 21 and 30 equals 210.
Frequently Asked Questions on LCM of 21 and 30
What is the LCM of 21 and 30?
List the methods used to find the LCM of 21 and 30.
If the LCM of 30 and 21 is 210, Find its GCF.
Since the LCM of 30 and 21 = 210
⇒ 210 × GCF(30, 21) = 630
Therefore, the greatest common factor (GCF) = 630/210 = 3.
Which of the following is the LCM of 21 and 30? 210, 5, 15, 16
What is the Least Perfect Square Divisible by 21 and 30?
LCM of 21 and 30 = 2 × 3 × 5 × 7 [Incomplete pair(s): 2, 3, 5, 7] ⇒ Least perfect square divisible by each 21 and 30 = LCM(21, 30) × 2 × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210] Therefore, 44100 is the required number.
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