LCM of 3 and 17

LCM of 3 and 17 is the smallest number among all common multiples of 3 and 17. The first few multiples of 3 and 17 are (3, 6, 9, 12, 15, 18, . . . ) and (17, 34, 51, 68, 85, 102, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 17 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 3 and 17 is 51.

Explanation:

The LCM of two non-zero integers, x(3) and y(17), is the smallest positive integer m(51) that is divisible by both x(3) and y(17) without any remainder.

The methods to find the LCM of 3 and 17 are explained below.

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

LCM of 3 and 17 by Listing Multiples

To calculate the LCM of 3 and 17 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, . . . ) and 17 (17, 34, 51, 68, 85, 102, . . . . )
• Step 2: The common multiples from the multiples of 3 and 17 are 51, 102, . . .
• Step 3: The smallest common multiple of 3 and 17 is 51.

∴ The least common multiple of 3 and 17 = 51.

LCM of 3 and 17 by Division Method

To calculate the LCM of 3 and 17 by the division method, we will divide the numbers(3, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 17.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 17. Write this prime number(3) on the left of the given numbers(3 and 17), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (3, 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 3 and 17 is the product of all prime numbers on the left, i.e. LCM(3, 17) by division method = 3 × 17 = 51.

LCM of 3 and 17 by Prime Factorization

Prime factorization of 3 and 17 is (3) = 3¹ and (17) = 17¹ respectively. LCM of 3 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 17¹ = 51.
Hence, the LCM of 3 and 17 by prime factorization is 51.

☛ Also Check:

• LCM of 9 and 24 - 72
• LCM of 35 and 49 - 245
• LCM of 60 and 90 - 180
• LCM of 14 and 18 - 126
• LCM of 9 and 27 - 27
• LCM of 12, 15 and 45 - 180
• LCM of 3, 9 and 18 - 18

FAQs on LCM of 3 and 17

What is the LCM of 3 and 17?

The LCM of 3 and 17 is 51. To find the LCM (least common multiple) of 3 and 17, we need to find the multiples of 3 and 17 (multiples of 3 = 3, 6, 9, 12 . . . . 51; multiples of 17 = 17, 34, 51, 68) and choose the smallest multiple that is exactly divisible by 3 and 17, i.e., 51.

What are the Methods to Find LCM of 3 and 17?

The commonly used methods to find the LCM of 3 and 17 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

How to Find the LCM of 3 and 17 by Prime Factorization?

To find the LCM of 3 and 17 using prime factorization, we will find the prime factors, (3 = 3) and (17 = 17). LCM of 3 and 17 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 17.
⇒ LCM of 3, 17 = 3¹ × 17¹ = 51.

If the LCM of 17 and 3 is 51, Find its GCF.

LCM(17, 3) × GCF(17, 3) = 17 × 3
Since the LCM of 17 and 3 = 51
⇒ 51 × GCF(17, 3) = 51
Therefore, the GCF = 51/51 = 1.

What is the Relation Between GCF and LCM of 3, 17?

The following equation can be used to express the relation between GCF and LCM of 3 and 17, i.e. GCF × LCM = 3 × 17.