LCM of 9 and 33

LCM of 9 and 33 is the smallest number among all common multiples of 9 and 33. The first few multiples of 9 and 33 are (9, 18, 27, 36, 45, 54, . . . ) and (33, 66, 99, 132, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 33 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 9 and 33 is 99.

Explanation:

The LCM of two non-zero integers, x(9) and y(33), is the smallest positive integer m(99) that is divisible by both x(9) and y(33) without any remainder.

Let's look at the different methods for finding the LCM of 9 and 33.

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

LCM of 9 and 33 by Prime Factorization

Prime factorization of 9 and 33 is (3 × 3) = 3² and (3 × 11) = 3¹ × 11¹ respectively. LCM of 9 and 33 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 11¹ = 99.
Hence, the LCM of 9 and 33 by prime factorization is 99.

LCM of 9 and 33 by Division Method

To calculate the LCM of 9 and 33 by the division method, we will divide the numbers(9, 33) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 33.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 33. Write this prime number(3) on the left of the given numbers(9 and 33), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 33) 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 9 and 33 is the product of all prime numbers on the left, i.e. LCM(9, 33) by division method = 3 × 3 × 11 = 99.

LCM of 9 and 33 by Listing Multiples

To calculate the LCM of 9 and 33 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, . . . ) and 33 (33, 66, 99, 132, . . . . )
• Step 2: The common multiples from the multiples of 9 and 33 are 99, 198, . . .
• Step 3: The smallest common multiple of 9 and 33 is 99.

∴ The least common multiple of 9 and 33 = 99.

☛ Also Check:

• LCM of 32 and 48 - 96
• LCM of 7, 11, 21 and 22 - 462
• LCM of 20 and 36 - 180
• LCM of 96 and 404 - 9696
• LCM of 23 and 69 - 69
• LCM of 12 and 15 - 60
• LCM of 12, 18 and 20 - 180

FAQs on LCM of 9 and 33

What is the LCM of 9 and 33?

The LCM of 9 and 33 is 99. To find the LCM of 9 and 33, we need to find the multiples of 9 and 33 (multiples of 9 = 9, 18, 27, 36 . . . . 99; multiples of 33 = 33, 66, 99, 132) and choose the smallest multiple that is exactly divisible by 9 and 33, i.e., 99.

If the LCM of 33 and 9 is 99, Find its GCF.

LCM(33, 9) × GCF(33, 9) = 33 × 9
Since the LCM of 33 and 9 = 99
⇒ 99 × GCF(33, 9) = 297
Therefore, the greatest common factor (GCF) = 297/99 = 3.

Which of the following is the LCM of 9 and 33? 99, 11, 10, 35

The value of LCM of 9, 33 is the smallest common multiple of 9 and 33. The number satisfying the given condition is 99.

What is the Least Perfect Square Divisible by 9 and 33?

The least number divisible by 9 and 33 = LCM(9, 33)
LCM of 9 and 33 = 3 × 3 × 11 [Incomplete pair(s): 11]
⇒ Least perfect square divisible by each 9 and 33 = LCM(9, 33) × 11 = 1089 [Square root of 1089 = √1089 = ±33]
Therefore, 1089 is the required number.

What are the Methods to Find LCM of 9 and 33?

The commonly used methods to find the LCM of 9 and 33 are:

• Division Method
• Listing Multiples
• Prime Factorization Method