LCM of 17 and 34 is 34. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. LCM of 17 and 34 is the smallest number among all common multiples of 17 and 34. The first few multiples of 17 and 34 are (17, 34, 51, 68, 85, 102, . . . ) and (34, 68, 102, 136, 170, . . . ) respectively.
Also read: Least common multiple
What is LCM of 17 and 34?
The answer to this question is 34. The LCM of 17 and 34 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 17 and 34, is the smallest positive integer 34 which is divisible by both 17 and 34 with no remainder.
How to Find LCM of 17 and 34?
LCM of 17 and 34 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 17 and 34 Using Prime Factorisation Method
The prime factorisation of 17 and 34, respectively, is given by:
17 = 171 and
34 = (2 × 17) = 21 × 171
LCM (17, 34) = 34
LCM of 17 and 34 Using Division Method
We’ll divide the numbers (17, 34) by their prime factors to get the LCM of 17 and 34 using the division method (preferably common). The LCM of 17 and 34 is calculated by multiplying these divisors.
| 2 | 17 | 34 |
| 17 | 17 | 17 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (17, 34) = 34
LCM of 17 and 34 Using Listing the Multiples
To calculate the LCM of 17 and 34 by listing out the common multiples, list the multiples as shown below.
| Multiples of 17 | Multiples of 34 |
| 17 | 34 |
| 34 | 68 |
| 51 | 102 |
| 68 | 136 |
| 85 | 170 |
The smallest common multiple of 17 and 34 is 34.
Therefore LCM (17, 34) = 34
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LCM of 17 and 34 Solved Example
Question: The GCD and LCM of two numbers are 17 and 34 respectively. If one number is 34, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 34 × p
⇒ p = (GCD × LCM)/34
⇒ p = (17 × 34)/34
⇒ p = 17
Therefore, the other number is 17.
Frequently Asked Questions on LCM of 17 and 34
What is the LCM of 17 and 34?
List the methods used to find the LCM of 17 and 34.
What is the Relation Between GCF and LCM of 17, 34?
If the LCM of 34 and 17 is 34, Find its GCF.
Since the LCM of 34 and 17 = 34
⇒ 34 × GCF(34, 17) = 578
Therefore, the GCF (greatest common factor) = 578/34 = 17.
What is the Least Perfect Square Divisible by 17 and 34?
LCM of 17 and 34 = 2 × 17 [Incomplete pair(s): 2, 17] ⇒ Least perfect square divisible by each 17 and 34 = LCM(17, 34) × 2 × 17 = 1156 [Square root of 1156 = √1156 = ±34] Therefore, 1156 is the required number.
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