LCM of 17 and 34
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. There are 3 commonly used methods to find LCM of 17 and 34  by division method, by listing multiples, and by prime factorization.
1.  LCM of 17 and 34 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 17 and 34?
Answer: LCM of 17 and 34 is 34.
Explanation:
The LCM of two nonzero integers, x(17) and y(34), is the smallest positive integer m(34) that is divisible by both x(17) and y(34) without any remainder.
Methods to Find LCM of 17 and 34
Let's look at the different methods for finding the LCM of 17 and 34.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 17 and 34 by Prime Factorization
Prime factorization of 17 and 34 is (17) = 17^{1} and (2 × 17) = 2^{1} × 17^{1} respectively. LCM of 17 and 34 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 17^{1} = 34.
Hence, the LCM of 17 and 34 by prime factorization is 34.
LCM of 17 and 34 by Division Method
To calculate the LCM of 17 and 34 by the division method, we will divide the numbers(17, 34) by their prime factors (preferably common). The product of these divisors gives the LCM of 17 and 34.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 17 and 34. Write this prime number(2) on the left of the given numbers(17 and 34), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (17, 34) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 17 and 34 is the product of all prime numbers on the left, i.e. LCM(17, 34) by division method = 2 × 17 = 34.
LCM of 17 and 34 by Listing Multiples
To calculate the LCM of 17 and 34 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 17 (17, 34, 51, 68, 85, 102, . . . ) and 34 (34, 68, 102, 136, 170, . . . . )
 Step 2: The common multiples from the multiples of 17 and 34 are 34, 68, . . .
 Step 3: The smallest common multiple of 17 and 34 is 34.
∴ The least common multiple of 17 and 34 = 34.
☛ Also Check:
 LCM of 7 and 17  119
 LCM of 2, 3 and 7  42
 LCM of 96 and 404  9696
 LCM of 16 and 22  176
 LCM of 12 and 30  60
 LCM of 8 and 13  104
 LCM of 6, 8 and 9  72
LCM of 17 and 34 Examples

Example 1: 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. 
Example 2: Find the smallest number that is divisible by 17 and 34 exactly.
Solution:
The smallest number that is divisible by 17 and 34 exactly is their LCM.
⇒ Multiples of 17 and 34: Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, . . . .
 Multiples of 34 = 34, 68, 102, 136, 170, 204, 238, . . . .
Therefore, the LCM of 17 and 34 is 34.

Example 3: Verify the relationship between GCF and LCM of 17 and 34.
Solution:
The relation between GCF and LCM of 17 and 34 is given as,
LCM(17, 34) × GCF(17, 34) = Product of 17, 34
Prime factorization of 17 and 34 is given as, 17 = (17) = 17^{1} and 34 = (2 × 17) = 2^{1} × 17^{1}
LCM(17, 34) = 34
GCF(17, 34) = 17
LHS = LCM(17, 34) × GCF(17, 34) = 34 × 17 = 578
RHS = Product of 17, 34 = 17 × 34 = 578
⇒ LHS = RHS = 578
Hence, verified.
FAQs on LCM of 17 and 34
What is the LCM of 17 and 34?
The LCM of 17 and 34 is 34. To find the least common multiple (LCM) of 17 and 34, we need to find the multiples of 17 and 34 (multiples of 17 = 17, 34, 51, 68; multiples of 34 = 34, 68, 102, 136) and choose the smallest multiple that is exactly divisible by 17 and 34, i.e., 34.
What is the Relation Between GCF and LCM of 17, 34?
The following equation can be used to express the relation between GCF and LCM of 17 and 34, i.e. GCF × LCM = 17 × 34.
If the LCM of 34 and 17 is 34, Find its GCF.
LCM(34, 17) × GCF(34, 17) = 34 × 17
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?
The least number divisible by 17 and 34 = LCM(17, 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.
What are the Methods to Find LCM of 17 and 34?
The commonly used methods to find the LCM of 17 and 34 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
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