LCM of 16 and 17

LCM of 16 and 17 is the smallest number among all common multiples of 16 and 17. The first few multiples of 16 and 17 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (17, 34, 51, 68, 85, 102, 119, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 17 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 16 and 17 is 272.

Explanation:

The LCM of two non-zero integers, x(16) and y(17), is the smallest positive integer m(272) that is divisible by both x(16) and y(17) without any remainder.

Let's look at the different methods for finding the LCM of 16 and 17.

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

LCM of 16 and 17 by Listing Multiples

To calculate the LCM of 16 and 17 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 16 (16, 32, 48, 64, 80, 96, 112, . . . ) and 17 (17, 34, 51, 68, 85, 102, 119, . . . . )
• Step 2: The common multiples from the multiples of 16 and 17 are 272, 544, . . .
• Step 3: The smallest common multiple of 16 and 17 is 272.

∴ The least common multiple of 16 and 17 = 272.

LCM of 16 and 17 by Division Method

To calculate the LCM of 16 and 17 by the division method, we will divide the numbers(16, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 17.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 17. Write this prime number(2) on the left of the given numbers(16 and 17), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 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 16 and 17 is the product of all prime numbers on the left, i.e. LCM(16, 17) by division method = 2 × 2 × 2 × 2 × 17 = 272.

LCM of 16 and 17 by Prime Factorization

Prime factorization of 16 and 17 is (2 × 2 × 2 × 2) = 2⁴ and (17) = 17¹ respectively. LCM of 16 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 17¹ = 272.
Hence, the LCM of 16 and 17 by prime factorization is 272.

☛ Also Check:

• LCM of 25 and 60 - 300
• LCM of 15, 30 and 90 - 90
• LCM of 8 and 14 - 56
• LCM of 28 and 42 - 84
• LCM of 25 and 16 - 400
• LCM of 21 and 30 - 210
• LCM of 36 and 64 - 576

FAQs on LCM of 16 and 17

What is the LCM of 16 and 17?

The LCM of 16 and 17 is 272. To find the least common multiple of 16 and 17, we need to find the multiples of 16 and 17 (multiples of 16 = 16, 32, 48, 64 . . . . 272; multiples of 17 = 17, 34, 51, 68 . . . . 272) and choose the smallest multiple that is exactly divisible by 16 and 17, i.e., 272.

What is the Least Perfect Square Divisible by 16 and 17?

The least number divisible by 16 and 17 = LCM(16, 17)
LCM of 16 and 17 = 2 × 2 × 2 × 2 × 17 [Incomplete pair(s): 17]
⇒ Least perfect square divisible by each 16 and 17 = LCM(16, 17) × 17 = 4624 [Square root of 4624 = √4624 = ±68]
Therefore, 4624 is the required number.

If the LCM of 17 and 16 is 272, Find its GCF.

LCM(17, 16) × GCF(17, 16) = 17 × 16
Since the LCM of 17 and 16 = 272
⇒ 272 × GCF(17, 16) = 272
Therefore, the GCF (greatest common factor) = 272/272 = 1.

What is the Relation Between GCF and LCM of 16, 17?

The following equation can be used to express the relation between GCF and LCM of 16 and 17, i.e. GCF × LCM = 16 × 17.

Which of the following is the LCM of 16 and 17? 3, 272, 10, 42

The value of LCM of 16, 17 is the smallest common multiple of 16 and 17. The number satisfying the given condition is 272.