LCM of 16 and 18

LCM of 16 and 18 is the smallest number among all common multiples of 16 and 18. The first few multiples of 16 and 18 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 18 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 16 and 18 is 144.

Explanation:

The LCM of two non-zero integers, x(16) and y(18), is the smallest positive integer m(144) that is divisible by both x(16) and y(18) without any remainder.

Let's look at the different methods for finding the LCM of 16 and 18.

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

LCM of 16 and 18 by Listing Multiples

To calculate the LCM of 16 and 18 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 18 (18, 36, 54, 72, . . . . )
• Step 2: The common multiples from the multiples of 16 and 18 are 144, 288, . . .
• Step 3: The smallest common multiple of 16 and 18 is 144.

∴ The least common multiple of 16 and 18 = 144.

LCM of 16 and 18 by Prime Factorization

Prime factorization of 16 and 18 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 3 × 3) = 2¹ × 3² respectively. LCM of 16 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3² = 144.
Hence, the LCM of 16 and 18 by prime factorization is 144.

LCM of 16 and 18 by Division Method

To calculate the LCM of 16 and 18 by the division method, we will divide the numbers(16, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 18.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 18. Write this prime number(2) on the left of the given numbers(16 and 18), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 18) 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 18 is the product of all prime numbers on the left, i.e. LCM(16, 18) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

☛ Also Check:

• LCM of 3, 4 and 7 - 84
• LCM of 6 and 7 - 42
• LCM of 12 and 28 - 84
• LCM of 36, 48 and 54 - 432
• LCM of 148 and 185 - 740
• LCM of 2, 5 and 6 - 30
• LCM of 64 and 72 - 576

FAQs on LCM of 16 and 18

What is the LCM of 16 and 18?

The LCM of 16 and 18 is 144. To find the LCM (least common multiple) of 16 and 18, we need to find the multiples of 16 and 18 (multiples of 16 = 16, 32, 48, 64 . . . . 144; multiples of 18 = 18, 36, 54, 72 . . . . 144) and choose the smallest multiple that is exactly divisible by 16 and 18, i.e., 144.

How to Find the LCM of 16 and 18 by Prime Factorization?

To find the LCM of 16 and 18 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (18 = 2 × 3 × 3). LCM of 16 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 18.
⇒ LCM of 16, 18 = 2⁴ × 3² = 144.

If the LCM of 18 and 16 is 144, Find its GCF.

LCM(18, 16) × GCF(18, 16) = 18 × 16
Since the LCM of 18 and 16 = 144
⇒ 144 × GCF(18, 16) = 288
Therefore, the greatest common factor = 288/144 = 2.

What are the Methods to Find LCM of 16 and 18?

The commonly used methods to find the LCM of 16 and 18 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

Which of the following is the LCM of 16 and 18? 15, 144, 50, 16

The value of LCM of 16, 18 is the smallest common multiple of 16 and 18. The number satisfying the given condition is 144.