LCM of 6 and 7 is 42. Among all common multiples of 6 and 7, the LCM of 6 and 7 is the smallest number. (6, 12, 18, 24, 30, 36, and so on) and (7, 14, 21, 28, 35, 42, 49, and so on) are the first few multiples of 6 and 7. The division technique, prime factorization, and listing multiples are the three most frequent ways for finding the LCM of 6 and 7. 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 6 and 7?
The answer to this question is 42. The LCM of 6 and 7 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 7, is the smallest positive integer 42 which is divisible by both 6 and 7 with no remainder.
How to Find LCM of 6 and 7?
LCM of 6 and 7 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 7 Using Prime Factorisation Method
The prime factorisation of 6 and 7, respectively, is given by:
6 = (2 × 3) = 2 × 3 and
(7) = 7
LCM (6, 7) = 42
LCM of 6 and 7 Using Division Method
We’ll divide the numbers (6, 7) by their prime factors to get the LCM of 6 and 7 using the division method (preferably common). The LCM of 6 and 7 is calculated by multiplying these divisors.
| 2 | 6 | 7 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (6, 7) = 42
LCM of 6 and 7 Using Listing the Multiples
To calculate the LCM of 6 and 7 by listing out the common multiples, list the multiples as shown below
| Multiples of 6 | Multiples of 7 |
| 6 | 7 |
| 12 | 14 |
| 18 | 21 |
| 24 | 28 |
| 30 | 35 |
| 36 | 42 |
| 42 | 49 |
The smallest common multiple of 6 and 7 is 42.
LCM (6, 7) = 42
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LCM of 6 and 7 Solved Example
Find the smallest number that is divisible by 6 and 7 exactly.
The smallest number that is divisible by 6 and 7 exactly is their LCM.
Multiples of 6 and 7:
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, . . . .
Multiples of 7 = 7, 14, 21, 28, 35, 42, . . . .
Therefore, the LCM of 6 and 7 is 42.
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