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LCM of 9 and 17

LCM of 9 and 17 is the smallest number among all common multiples of 9 and 17. The first few multiples of 9 and 17 are (9, 18, 27, 36, 45, . . . ) and (17, 34, 51, 68, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 17 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 9 and 17
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 9 and 17?

Answer: LCM of 9 and 17 is 153.

Explanation:

The LCM of two non-zero integers, x(9) and y(17), is the smallest positive integer m(153) that is divisible by both x(9) and y(17) without any remainder.

Methods to Find LCM of 9 and 17

Let's look at the different methods for finding the LCM of 9 and 17.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 9 and 17 by Prime Factorization

Prime factorization of 9 and 17 is (3 × 3) = 3² and (17) = 17¹ respectively. LCM of 9 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 17¹ = 153.
Hence, the LCM of 9 and 17 by prime factorization is 153.

LCM of 9 and 17 by Listing Multiples

To calculate the LCM of 9 and 17 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, . . . ) and 17 (17, 34, 51, 68, . . . . )
Step 2: The common multiples from the multiples of 9 and 17 are 153, 306, . . .
Step 3: The smallest common multiple of 9 and 17 is 153.

∴ The least common multiple of 9 and 17 = 153.

LCM of 9 and 17 by Division Method

To calculate the LCM of 9 and 17 by the division method, we will divide the numbers(9, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 17.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 17. Write this prime number(3) on the left of the given numbers(9 and 17), separated as per the ladder arrangement.
Step 2: If any of the given numbers (9, 17) is a multiple of 3, divide it by 3 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 9 and 17 is the product of all prime numbers on the left, i.e. LCM(9, 17) by division method = 3 × 3 × 17 = 153.

☛ Also Check:

LCM of 9 and 17 Examples

Example 1: Verify the relationship between GCF and LCM of 9 and 17.

Solution:

The relation between GCF and LCM of 9 and 17 is given as,
LCM(9, 17) × GCF(9, 17) = Product of 9, 17
Prime factorization of 9 and 17 is given as, 9 = (3 × 3) = 3² and 17 = (17) = 17¹
LCM(9, 17) = 153
GCF(9, 17) = 1
LHS = LCM(9, 17) × GCF(9, 17) = 153 × 1 = 153
RHS = Product of 9, 17 = 9 × 17 = 153
⇒ LHS = RHS = 153
Hence, verified.
Example 2: The product of two numbers is 153. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 153
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 153/1
Therefore, the LCM is 153.
The probable combination for the given case is LCM(9, 17) = 153.
Example 3: Find the smallest number that is divisible by 9 and 17 exactly.

Solution:

The value of LCM(9, 17) will be the smallest number that is exactly divisible by 9 and 17.
⇒ Multiples of 9 and 17:
- Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 135, 144, 153, . . . .
- Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, . . . ., 119, 136, 153, . . . .
Therefore, the LCM of 9 and 17 is 153.

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FAQs on LCM of 9 and 17

What is the LCM of 9 and 17?

The LCM of 9 and 17 is 153. To find the least common multiple (LCM) of 9 and 17, we need to find the multiples of 9 and 17 (multiples of 9 = 9, 18, 27, 36 . . . . 153; multiples of 17 = 17, 34, 51, 68 . . . . 153) and choose the smallest multiple that is exactly divisible by 9 and 17, i.e., 153.

How to Find the LCM of 9 and 17 by Prime Factorization?

To find the LCM of 9 and 17 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (17 = 17). LCM of 9 and 17 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 17.
⇒ LCM of 9, 17 = 3² × 17¹ = 153.

Which of the following is the LCM of 9 and 17? 153, 28, 27, 3

The value of LCM of 9, 17 is the smallest common multiple of 9 and 17. The number satisfying the given condition is 153.

What is the Relation Between GCF and LCM of 9, 17?

The following equation can be used to express the relation between GCF and LCM of 9 and 17, i.e. GCF × LCM = 9 × 17.

If the LCM of 17 and 9 is 153, Find its GCF.

LCM(17, 9) × GCF(17, 9) = 17 × 9
Since the LCM of 17 and 9 = 153
⇒ 153 × GCF(17, 9) = 153
Therefore, the GCF = 153/153 = 1.

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