LCM of 12 and 17 is 204. LCM is the short form for Least/Lowest Common Multiple is the smallest positive number that is divisible by the given numbers. Consider the example for finding the LCM of 12 and 17. The answer is 204. 204 is divisible by both 12 and 17. Even 1020 is divisible by 12 and 17, however it is not the LCM for 12 and 17. The smaller number than 1020 is 204 which is divisible by both 12 and 17. Hence 204 is the Least Common Multiple for 12 and 17. You can use the Prime Factorization and Division method to find the LCM of any 2 numbers.
What is LCM of 12 and 17
The Least Common Multiple or Lowest Common Multiple of 12 and 17 is 204.
How to Find LCM of 12 and 17?
LCM of 12 and 17 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 17 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 12 and 17 can be expressed as;
12 = 2 × 2 × 3
17 = 1 × 17
17 is a prime number which is multiplied by the prime factors of 12 to get the LCM.
LCM (12, 17) = 2 × 2 × 3 × 17 = 204
LCM of 12 and 17 Using Division Method
In the Division Method, the numbers 12 and 17 are divided by prime divisors. Since 12 and 17 do not have common prime factors, the factors of 17 with the prime factors of 12 are multiplied to get the LCM.
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2 |
12 |
17 |
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2 |
6 |
17 |
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3 |
3 |
17 |
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17 |
1 |
17 |
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× |
1 |
1 |
LCM (12, 17) = 2 × 2 × 3 × 17 = 204
LCM of 12 and 17 Using Listing the Multiples
By listing all the multiples of 12 and 17 numbers, we can get the LCM. Below is the list of multiples for 12 and 17
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228
Multiples of 17:
17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238
LCM (12, 17) = 204
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 12 and 17?
Answer: 204 is the smallest number that is divisible by both 12 and 17.
What is the LCM for 6, 12 and 17?
Answer: LCM for 6, 12 and 17 is 204 as 6 is the factor of 12.
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