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.

Answer: LCM of 7 and 17 is 119.

Explanation:

The LCM of two non-zero 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.

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) = 7¹ and (17) = 17¹ respectively. LCM of 7 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 7¹ × 17¹ = 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

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 = 7¹ × 17¹ = 119.