LCM of 34 and 51 is 102. LCM is the abbreviation for Lowest/Least Common Multiple is the least common multiple in the given set of common multiples. Consider the example for finding the LCM of 34 and 51. The answer is 102. 102 is divisible by both 34 and 51. Even 204 is divisible by 34 and 51, however it is not the LCM for 34 and 51. The smaller number than 204 is 102 which is divisible by both 34 and 51. Hence 102 is the Least Common Multiple for 34 and 51. You can refer to LCM with Examples for better understanding.
What is LCM of 34 and 51
The Least Common Multiple or Lowest Common Multiple of 34 and 51 is 102.
How to Find LCM of 34 and 51?
LCM of 34 and 51 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 34 and 51 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 34 and 51 can be expressed as;
34 = 2 × 17
51 = 3 × 17
17 is the common prime factor of 34 and 51, this is multiplied by the other prime factors 2 and 3 to get the LCM.
LCM (34, 51) = 2 × 3 × 17 = 102
LCM of 34 and 51 Using Division Method
In the Division Method,
- Dividing 34 and 51 by smallest common prime factors.
- Completing the division with other prime factors till the reminders are 1.
- Product of the prime divisors is the LCM.
|
2 |
34 |
51 |
|
3 |
17 |
51 |
|
17 |
17 |
17 |
|
× |
1 |
1 |
LCM (34, 51) = 2 × 3 × 17 = 102
LCM of 34 and 51 Using Listing the Multiples
By listing all the multiples of 34 and 51 we can get the LCM. Below is the list of multiples for 34 and 51
|
Multiples of 34 |
Multiples of 51 |
|
34 |
51 |
|
68 |
102 |
|
102 |
153 |
|
136 |
204 |
LCM (34, 51) = 102
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 34 and 51?
Answer: 102 is the smallest number that is divisible by both 34 and 51.
What is the LCM of 17, 34 and 51?
Answer: The LCM of 17, 34 and 51 is 102 as 17 is the factor of 34 and 51.
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