LCM of 17 and 19

LCM of 17 and 19 is the smallest number among all common multiples of 17 and 19. The first few multiples of 17 and 19 are (17, 34, 51, 68, 85, 102, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively. There are 3 commonly used methods to find LCM of 17 and 19 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 17 and 19 is 323.

Explanation:

The LCM of two non-zero integers, x(17) and y(19), is the smallest positive integer m(323) that is divisible by both x(17) and y(19) without any remainder.

Let's look at the different methods for finding the LCM of 17 and 19.

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

LCM of 17 and 19 by Prime Factorization

Prime factorization of 17 and 19 is (17) = 17¹ and (19) = 19¹ respectively. LCM of 17 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 17¹ × 19¹ = 323.
Hence, the LCM of 17 and 19 by prime factorization is 323.

LCM of 17 and 19 by Listing Multiples

To calculate the LCM of 17 and 19 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 19 (19, 38, 57, 76, 95, . . . . )
• Step 2: The common multiples from the multiples of 17 and 19 are 323, 646, . . .
• Step 3: The smallest common multiple of 17 and 19 is 323.

∴ The least common multiple of 17 and 19 = 323.

LCM of 17 and 19 by Division Method

To calculate the LCM of 17 and 19 by the division method, we will divide the numbers(17, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 17 and 19.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 17 and 19. Write this prime number(17) on the left of the given numbers(17 and 19), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (17, 19) is a multiple of 17, divide it by 17 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 19 is the product of all prime numbers on the left, i.e. LCM(17, 19) by division method = 17 × 19 = 323.

☛ Also Check:

• LCM of 15, 20 and 30 - 60
• LCM of 54 and 90 - 270
• LCM of 24 and 36 - 72
• LCM of 8 and 14 - 56
• LCM of 18 and 32 - 288
• LCM of 6 and 10 - 30
• LCM of 4 and 12 - 12

FAQs on LCM of 17 and 19

What is the LCM of 17 and 19?

The LCM of 17 and 19 is 323. To find the LCM (least common multiple) of 17 and 19, we need to find the multiples of 17 and 19 (multiples of 17 = 17, 34, 51, 68 . . . . 323; multiples of 19 = 19, 38, 57, 76 . . . . 323) and choose the smallest multiple that is exactly divisible by 17 and 19, i.e., 323.

Which of the following is the LCM of 17 and 19? 3, 323, 15, 35

The value of LCM of 17, 19 is the smallest common multiple of 17 and 19. The number satisfying the given condition is 323.

What is the Least Perfect Square Divisible by 17 and 19?

The least number divisible by 17 and 19 = LCM(17, 19)
LCM of 17 and 19 = 17 × 19 [Incomplete pair(s): 17, 19]
⇒ Least perfect square divisible by each 17 and 19 = LCM(17, 19) × 17 × 19 = 104329 [Square root of 104329 = √104329 = ±323]
Therefore, 104329 is the required number.

What are the Methods to Find LCM of 17 and 19?

The commonly used methods to find the LCM of 17 and 19 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

If the LCM of 19 and 17 is 323, Find its GCF.

LCM(19, 17) × GCF(19, 17) = 19 × 17
Since the LCM of 19 and 17 = 323
⇒ 323 × GCF(19, 17) = 323
Therefore, the greatest common factor (GCF) = 323/323 = 1.