LCM of 9 and 16

LCM of 9 and 16 is the smallest number among all common multiples of 9 and 16. The first few multiples of 9 and 16 are (9, 18, 27, 36, 45, 54, 63, . . . ) and (16, 32, 48, 64, 80, 96, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 16 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 9 and 16 is 144.

Explanation:

The LCM of two non-zero integers, x(9) and y(16), is the smallest positive integer m(144) that is divisible by both x(9) and y(16) without any remainder.

Let's look at the different methods for finding the LCM of 9 and 16.

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

LCM of 9 and 16 by Division Method

To calculate the LCM of 9 and 16 by the division method, we will divide the numbers(9, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 16.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 16. Write this prime number(2) on the left of the given numbers(9 and 16), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 16) 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 9 and 16 is the product of all prime numbers on the left, i.e. LCM(9, 16) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

LCM of 9 and 16 by Listing Multiples

To calculate the LCM of 9 and 16 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, 63, . . . ) and 16 (16, 32, 48, 64, 80, 96, . . . . )
• Step 2: The common multiples from the multiples of 9 and 16 are 144, 288, . . .
• Step 3: The smallest common multiple of 9 and 16 is 144.

∴ The least common multiple of 9 and 16 = 144.

LCM of 9 and 16 by Prime Factorization

Prime factorization of 9 and 16 is (3 × 3) = 3² and (2 × 2 × 2 × 2) = 2⁴ respectively. LCM of 9 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3² = 144.
Hence, the LCM of 9 and 16 by prime factorization is 144.

☛ Also Check:

• LCM of 18, 24 and 32 - 288
• LCM of 6 and 14 - 42
• LCM of 8 and 14 - 56
• LCM of 15 and 27 - 135
• LCM of 21 and 27 - 189
• LCM of 18 and 28 - 252
• LCM of 5, 9 and 15 - 45

FAQs on LCM of 9 and 16

What is the LCM of 9 and 16?

The LCM of 9 and 16 is 144. To find the LCM of 9 and 16, we need to find the multiples of 9 and 16 (multiples of 9 = 9, 18, 27, 36 . . . . 144; multiples of 16 = 16, 32, 48, 64 . . . . 144) and choose the smallest multiple that is exactly divisible by 9 and 16, i.e., 144.

What is the Least Perfect Square Divisible by 9 and 16?

The least number divisible by 9 and 16 = LCM(9, 16)
LCM of 9 and 16 = 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 9 and 16 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

How to Find the LCM of 9 and 16 by Prime Factorization?

To find the LCM of 9 and 16 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (16 = 2 × 2 × 2 × 2). LCM of 9 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 16.
⇒ LCM of 9, 16 = 2⁴ × 3² = 144.

What is the Relation Between GCF and LCM of 9, 16?

The following equation can be used to express the relation between GCF and LCM of 9 and 16, i.e. GCF × LCM = 9 × 16.

If the LCM of 16 and 9 is 144, Find its GCF.

LCM(16, 9) × GCF(16, 9) = 16 × 9
Since the LCM of 16 and 9 = 144
⇒ 144 × GCF(16, 9) = 144
Therefore, the greatest common factor (GCF) = 144/144 = 1.