LCM of 7 and 17
LCM of 7 and 17 is the smallest number among all common multiples of 7 and 17. The first few multiples of 7 and 17 are (7, 14, 21, 28, 35, 42, . . . ) and (17, 34, 51, 68, 85, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 17  by division method, by prime factorization, and by listing multiples.
1.  LCM of 7 and 17 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 7 and 17?
Answer: LCM of 7 and 17 is 119.
Explanation:
The LCM of two nonzero integers, x(7) and y(17), is the smallest positive integer m(119) that is divisible by both x(7) and y(17) without any remainder.
Methods to Find LCM of 7 and 17
The methods to find the LCM of 7 and 17 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 7 and 17 by Division Method
To calculate the LCM of 7 and 17 by the division method, we will divide the numbers(7, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 17.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 17. Write this prime number(7) on the left of the given numbers(7 and 17), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (7, 17) is a multiple of 7, divide it by 7 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 7 and 17 is the product of all prime numbers on the left, i.e. LCM(7, 17) by division method = 7 × 17 = 119.
LCM of 7 and 17 by Listing Multiples
To calculate the LCM of 7 and 17 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, . . . ) and 17 (17, 34, 51, 68, 85, . . . . )
 Step 2: The common multiples from the multiples of 7 and 17 are 119, 238, . . .
 Step 3: The smallest common multiple of 7 and 17 is 119.
∴ The least common multiple of 7 and 17 = 119.
LCM of 7 and 17 by Prime Factorization
Prime factorization of 7 and 17 is (7) = 7^{1} and (17) = 17^{1} respectively. LCM of 7 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 7^{1} × 17^{1} = 119.
Hence, the LCM of 7 and 17 by prime factorization is 119.
☛ Also Check:
 LCM of 8, 10 and 15  120
 LCM of 8 and 20  40
 LCM of 4, 7 and 8  56
 LCM of 2 and 12  12
 LCM of 45 and 90  90
 LCM of 80 and 120  240
 LCM of 5 and 30  30
LCM of 7 and 17 Examples

Example 1: Find the smallest number that is divisible by 7 and 17 exactly.
Solution:
The value of LCM(7, 17) will be the smallest number that is exactly divisible by 7 and 17.
⇒ Multiples of 7 and 17: Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 91, 98, 105, 112, 119, . . . .
 Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, . . . ., 51, 68, 85, 102, 119, . . . .
Therefore, the LCM of 7 and 17 is 119.

Example 2: The GCD and LCM of two numbers are 1 and 119 respectively. If one number is 17, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 17 × z
⇒ z = (GCD × LCM)/17
⇒ z = (1 × 119)/17
⇒ z = 7
Therefore, the other number is 7. 
Example 3: The product of two numbers is 119. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 119
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 119/1
Therefore, the LCM is 119.
The probable combination for the given case is LCM(7, 17) = 119.
FAQs on LCM of 7 and 17
What is the LCM of 7 and 17?
The LCM of 7 and 17 is 119. To find the LCM (least common multiple) of 7 and 17, we need to find the multiples of 7 and 17 (multiples of 7 = 7, 14, 21, 28 . . . . 119; multiples of 17 = 17, 34, 51, 68 . . . . 119) and choose the smallest multiple that is exactly divisible by 7 and 17, i.e., 119.
What is the Relation Between GCF and LCM of 7, 17?
The following equation can be used to express the relation between GCF and LCM of 7 and 17, i.e. GCF × LCM = 7 × 17.
If the LCM of 17 and 7 is 119, Find its GCF.
LCM(17, 7) × GCF(17, 7) = 17 × 7
Since the LCM of 17 and 7 = 119
⇒ 119 × GCF(17, 7) = 119
Therefore, the greatest common factor (GCF) = 119/119 = 1.
What are the Methods to Find LCM of 7 and 17?
The commonly used methods to find the LCM of 7 and 17 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
How to Find the LCM of 7 and 17 by Prime Factorization?
To find the LCM of 7 and 17 using prime factorization, we will find the prime factors, (7 = 7) and (17 = 17). LCM of 7 and 17 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 17.
⇒ LCM of 7, 17 = 7^{1} × 17^{1} = 119.
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