LCM of 12 and 17

LCM of 12 and 17 is the smallest number among all common multiples of 12 and 17. The first few multiples of 12 and 17 are (12, 24, 36, 48, 60, 72, . . . ) and (17, 34, 51, 68, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 17 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 12 and 17 is 204.

Explanation:

The LCM of two non-zero integers, x(12) and y(17), is the smallest positive integer m(204) that is divisible by both x(12) and y(17) without any remainder.

The methods to find the LCM of 12 and 17 are explained below.

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

LCM of 12 and 17 by Prime Factorization

Prime factorization of 12 and 17 is (2 × 2 × 3) = 2² × 3¹ and (17) = 17¹ respectively. LCM of 12 and 17 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 17¹ = 204.
Hence, the LCM of 12 and 17 by prime factorization is 204.

LCM of 12 and 17 by Division Method

To calculate the LCM of 12 and 17 by the division method, we will divide the numbers(12, 17) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 17.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 17. Write this prime number(2) on the left of the given numbers(12 and 17), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 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 12 and 17 is the product of all prime numbers on the left, i.e. LCM(12, 17) by division method = 2 × 2 × 3 × 17 = 204.

LCM of 12 and 17 by Listing Multiples

To calculate the LCM of 12 and 17 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 17 (17, 34, 51, 68, . . . . )
• Step 2: The common multiples from the multiples of 12 and 17 are 204, 408, . . .
• Step 3: The smallest common multiple of 12 and 17 is 204.

∴ The least common multiple of 12 and 17 = 204.

☛ Also Check:

• LCM of 150 and 180 - 900
• LCM of 15 and 90 - 90
• LCM of 15 and 60 - 60
• LCM of 15 and 45 - 45
• LCM of 15 and 40 - 120
• LCM of 15 and 35 - 105
• LCM of 15 and 30 - 30

FAQs on LCM of 12 and 17

What is the LCM of 12 and 17?

The LCM of 12 and 17 is 204. To find the least common multiple of 12 and 17, we need to find the multiples of 12 and 17 (multiples of 12 = 12, 24, 36, 48 . . . . 204; multiples of 17 = 17, 34, 51, 68 . . . . 204) and choose the smallest multiple that is exactly divisible by 12 and 17, i.e., 204.

What is the Least Perfect Square Divisible by 12 and 17?

The least number divisible by 12 and 17 = LCM(12, 17)
LCM of 12 and 17 = 2 × 2 × 3 × 17 [Incomplete pair(s): 3, 17]
⇒ Least perfect square divisible by each 12 and 17 = LCM(12, 17) × 3 × 17 = 10404 [Square root of 10404 = √10404 = ±102]
Therefore, 10404 is the required number.

If the LCM of 17 and 12 is 204, Find its GCF.

LCM(17, 12) × GCF(17, 12) = 17 × 12
Since the LCM of 17 and 12 = 204
⇒ 204 × GCF(17, 12) = 204
Therefore, the GCF (greatest common factor) = 204/204 = 1.

How to Find the LCM of 12 and 17 by Prime Factorization?

To find the LCM of 12 and 17 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (17 = 17). LCM of 12 and 17 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 17.
⇒ LCM of 12, 17 = 2² × 3¹ × 17¹ = 204.

What is the Relation Between GCF and LCM of 12, 17?

The following equation can be used to express the relation between GCF and LCM of 12 and 17, i.e. GCF × LCM = 12 × 17.