LCM of 17 and 6 is 102. Least Common Multiple or the Lowest Common Multiple which is usually used as LCM, is the common multiple, which is also the smallest, for a given set of numbers. Here 17 and 6 is the given set of numbers, 102 is the first or smallest or least number that is common in the set of multiples of 17 and 6. The LCM can also be referred to as LCD which is Least Common Divisor and for (17, 6) it is 102. You can refer to the LCM with Examples for more understanding.
What is LCM of 17 and 6
The Least Common Multiple or Lowest Common Multiple of 17 and 6 is 102.
How to Find LCM of 17 and 6?
LCM of 17 and 6 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 17 and 6 Using Prime Factorisation Method
In the Prime Factorisation method for 17 and 6, both the numbers are expressed as a product of prime numbers. They are
17 = 1 × 17
6 = 2 × 3
The LCM will be the product of all these prime factors.
LCM (17, 6) = 2 × 3 × 17 = 102
LCM of 17 and 6 Using Division Method
In the Division Method, these simple steps are followed
Step1: Divise the numbers 6 and 17 with the smallest prime factor which is 2.
Step 2: Complete the division by taking the divisor as the next lowest prime factor
Step 3: The division is done once the remainders become 1.
Step 4: Product of the divisors form the LCM.
|
2 |
17 |
6 |
|
3 |
17 |
3 |
|
17 |
17 |
1 |
|
× |
1 |
1 |
LCM (17, 6) = 17 × 3 × 2 = 102.
LCM of 17 and 6 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 17 and 6
Multiples of 17:
17, 34, 51, 68, 85,102, 119, 136, 153, 170….
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114…
LCM (17, 6) = 102
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 17 and 6?
Answer: 102 is the smallest number that is divisible by (17, 6).
What is the Greatest Common Divisor for 17 and 6?
Answer: Greatest Common Divisor for 17 and 6 is 1.
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