LCM of 6 and 9

LCM of 6 and 9 is the smallest number among all common multiples of 6 and 9. The first few multiples of 6 and 9 are (6, 12, 18, 24, 30, . . . ) and (9, 18, 27, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 9 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 6 and 9 is 18.

Explanation:

The LCM of two non-zero integers, x(6) and y(9), is the smallest positive integer m(18) that is divisible by both x(6) and y(9) without any remainder.

The methods to find the LCM of 6 and 9 are explained below.

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

LCM of 6 and 9 by Division Method

To calculate the LCM of 6 and 9 by the division method, we will divide the numbers(6, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 9.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 9. Write this prime number(2) on the left of the given numbers(6 and 9), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 9) 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 6 and 9 is the product of all prime numbers on the left, i.e. LCM(6, 9) by division method = 2 × 3 × 3 = 18.

LCM of 6 and 9 by Listing Multiples

To calculate the LCM of 6 and 9 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, . . . ) and 9 (9, 18, 27, 36, . . . . )
• Step 2: The common multiples from the multiples of 6 and 9 are 18, 36, . . .
• Step 3: The smallest common multiple of 6 and 9 is 18.

∴ The least common multiple of 6 and 9 = 18.

LCM of 6 and 9 by Prime Factorization

Prime factorization of 6 and 9 is (2 × 3) = 2¹ × 3¹ and (3 × 3) = 3² respectively. LCM of 6 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² = 18.
Hence, the LCM of 6 and 9 by prime factorization is 18.

☛ Also Check:

• LCM of 32 and 64 - 64
• LCM of 36, 60 and 72 - 360
• LCM of 15 and 40 - 120
• LCM of 15, 20 and 25 - 300
• LCM of 12 and 30 - 60
• LCM of 3, 5 and 11 - 165
• LCM of 10 and 15 - 30

FAQs on LCM of 6 and 9

What is the LCM of 6 and 9?

The LCM of 6 and 9 is 18. To find the LCM (least common multiple) of 6 and 9, we need to find the multiples of 6 and 9 (multiples of 6 = 6, 12, 18, 24; multiples of 9 = 9, 18, 27, 36) and choose the smallest multiple that is exactly divisible by 6 and 9, i.e., 18.

What is the Least Perfect Square Divisible by 6 and 9?

The least number divisible by 6 and 9 = LCM(6, 9)
LCM of 6 and 9 = 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 6 and 9 = LCM(6, 9) × 2 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.

What are the Methods to Find LCM of 6 and 9?

The commonly used methods to find the LCM of 6 and 9 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

Which of the following is the LCM of 6 and 9? 16, 18, 11, 12

The value of LCM of 6, 9 is the smallest common multiple of 6 and 9. The number satisfying the given condition is 18.

If the LCM of 9 and 6 is 18, Find its GCF.

LCM(9, 6) × GCF(9, 6) = 9 × 6
Since the LCM of 9 and 6 = 18
⇒ 18 × GCF(9, 6) = 54
Therefore, the greatest common factor (GCF) = 54/18 = 3.