LCM of 7 and 21 is 21. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. LCM of 7 and 21 is the smallest number among all common multiples of 7 and 21. The first few multiples of 7 and 21 are (7, 14, 21, 28, 35, 42, 49, . . . ) and (21, 42, 63, 84, 105, 126, 147, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 21 – by listing multiples, by prime factorization, and by division method.
What is LCM of 7 and 21?
The answer to this question is 21. The LCM of 7 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 7 and 21, is the smallest positive integer 21 which is divisible by both 7 and 21 with no remainder.
Also read: Least common multiple
How to Find LCM of 7 and 21?
LCM of 7 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7 and 21 Using Prime Factorisation Method
The prime factorisation of 7 and 21, respectively, is given by:
(7) = 71 and
21 = (3 × 7) = 31 × 71
LCM (7, 21) = 21
LCM of 7 and 21 Using Division Method
We’ll divide the numbers (7, 21) by their prime factors to get the LCM of 7 and 21 using the division method (preferably common). The LCM of 7 and 21 is calculated by multiplying these divisors.
| 3 | 7 | 21 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (7, 21) = 21
LCM of 7 and 21 Using Listing the Multiples
To calculate the LCM of 7 and 21 by listing out the common multiples, list the multiples as shown below.
| Multiples of 7 | Multiples of 21 |
| 7 | 21 |
| 14 | 42 |
| 21 | 63 |
| 28 | 36 |
| 35 | 84 |
| 42 | 105 |
| 49 | 63 |
| 56 | 126 |
| 63 | 147 |
The smallest common multiple of 7 and 21 is 21.
LCM (7, 21) = 21
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LCM of 7 and 21 Solved Example
The GCD and LCM of two numbers are 7 and 21 respectively. If one number is 7, find the other number.
Solution:
Let the other number be m.
GCD × LCM = 7 × m
⇒ m = (GCD × LCM)/7
⇒ m = (7 × 21)/7
⇒ m = 21
Therefore, the other number is 21.
Frequently Asked Questions on LCM of 7 and 21
What is the LCM of 7 and 21?
What is the Relation Between GCF and LCM of 7, 21?
How to Find the LCM of 7 and 21 by Prime Factorization?
⇒ LCM of 7, 21 = 31 × 71 = 21.
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