LCM of 18 and 17

LCM of 18 and 17 is the smallest number among all common multiples of 18 and 17. The first few multiples of 18 and 17 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (17, 34, 51, 68, 85, 102, 119, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 17 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 18 and 17 is 306.

Explanation:

The LCM of two non-zero integers, x(18) and y(17), is the smallest positive integer m(306) that is divisible by both x(18) and y(17) without any remainder.

The methods to find the LCM of 18 and 17 are explained below.

• By Listing Multiples
• By Prime Factorization Method
• By Division Method

LCM of 18 and 17 by Listing Multiples

To calculate the LCM of 18 and 17 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 18 (18, 36, 54, 72, 90, 108, 126, . . . ) and 17 (17, 34, 51, 68, 85, 102, 119, . . . . )
• Step 2: The common multiples from the multiples of 18 and 17 are 306, 612, . . .
• Step 3: The smallest common multiple of 18 and 17 is 306.

∴ The least common multiple of 18 and 17 = 306.

LCM of 18 and 17 by Prime Factorization

Prime factorization of 18 and 17 is (2 × 3 × 3) = 2¹ × 3² and (17) = 17¹ respectively. LCM of 18 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 17¹ = 306.
Hence, the LCM of 18 and 17 by prime factorization is 306.

LCM of 18 and 17 by Division Method

To calculate the LCM of 18 and 17 by the division method, we will divide the numbers(18, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 17.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 17. Write this prime number(2) on the left of the given numbers(18 and 17), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 17) 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 18 and 17 is the product of all prime numbers on the left, i.e. LCM(18, 17) by division method = 2 × 3 × 3 × 17 = 306.

☛ Also Check:

• LCM of 4, 12 and 16 - 48
• LCM of 6 and 11 - 66
• LCM of 7, 11, 21 and 22 - 462
• LCM of 48, 56 and 72 - 1008
• LCM of 5 and 11 - 55
• LCM of 36 and 60 - 180
• LCM of 9 and 24 - 72

FAQs on LCM of 18 and 17

What is the LCM of 18 and 17?

The LCM of 18 and 17 is 306. To find the LCM of 18 and 17, we need to find the multiples of 18 and 17 (multiples of 18 = 18, 36, 54, 72 . . . . 306; multiples of 17 = 17, 34, 51, 68 . . . . 306) and choose the smallest multiple that is exactly divisible by 18 and 17, i.e., 306.

Which of the following is the LCM of 18 and 17? 35, 28, 306, 27

The value of LCM of 18, 17 is the smallest common multiple of 18 and 17. The number satisfying the given condition is 306.

If the LCM of 17 and 18 is 306, Find its GCF.

LCM(17, 18) × GCF(17, 18) = 17 × 18
Since the LCM of 17 and 18 = 306
⇒ 306 × GCF(17, 18) = 306
Therefore, the GCF = 306/306 = 1.

What are the Methods to Find LCM of 18 and 17?

The commonly used methods to find the LCM of 18 and 17 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

How to Find the LCM of 18 and 17 by Prime Factorization?

To find the LCM of 18 and 17 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (17 = 17). LCM of 18 and 17 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 17.
⇒ LCM of 18, 17 = 2¹ × 3² × 17¹ = 306.