LCM of 17 and 51

LCM of 17 and 51 is the smallest number among all common multiples of 17 and 51. The first few multiples of 17 and 51 are (17, 34, 51, 68, 85, 102, 119, . . . ) and (51, 102, 153, 204, 255, . . . ) respectively. There are 3 commonly used methods to find LCM of 17 and 51 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 17 and 51 is 51.

Explanation:

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

Let's look at the different methods for finding the LCM of 17 and 51.

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

LCM of 17 and 51 by Listing Multiples

To calculate the LCM of 17 and 51 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, 119, . . . ) and 51 (51, 102, 153, 204, 255, . . . . )
• Step 2: The common multiples from the multiples of 17 and 51 are 51, 102, . . .
• Step 3: The smallest common multiple of 17 and 51 is 51.

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

LCM of 17 and 51 by Division Method

To calculate the LCM of 17 and 51 by the division method, we will divide the numbers(17, 51) by their prime factors (preferably common). The product of these divisors gives the LCM of 17 and 51.

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

LCM of 17 and 51 by Prime Factorization

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

☛ Also Check:

• LCM of 2 and 9 - 18
• LCM of 50 and 60 - 300
• LCM of 8, 12 and 16 - 48
• LCM of 2, 6 and 8 - 24
• LCM of 4 and 7 - 28
• LCM of 48, 56 and 72 - 1008
• LCM of 200 and 300 - 600

FAQs on LCM of 17 and 51

What is the LCM of 17 and 51?

The LCM of 17 and 51 is 51. To find the least common multiple of 17 and 51, we need to find the multiples of 17 and 51 (multiples of 17 = 17, 34, 51, 68; multiples of 51 = 51, 102, 153, 204) and choose the smallest multiple that is exactly divisible by 17 and 51, i.e., 51.

Which of the following is the LCM of 17 and 51? 40, 51, 16, 42

The value of LCM of 17, 51 is the smallest common multiple of 17 and 51. The number satisfying the given condition is 51.

What is the Least Perfect Square Divisible by 17 and 51?

The least number divisible by 17 and 51 = LCM(17, 51)
LCM of 17 and 51 = 3 × 17 [Incomplete pair(s): 3, 17]
⇒ Least perfect square divisible by each 17 and 51 = LCM(17, 51) × 3 × 17 = 2601 [Square root of 2601 = √2601 = ±51]
Therefore, 2601 is the required number.

How to Find the LCM of 17 and 51 by Prime Factorization?

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

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

LCM(51, 17) × GCF(51, 17) = 51 × 17
Since the LCM of 51 and 17 = 51
⇒ 51 × GCF(51, 17) = 867
Therefore, the greatest common factor = 867/51 = 17.