LCM of 8 and 9

LCM of 8 and 9 is the smallest number among all common multiples of 8 and 9. The first few multiples of 8 and 9 are (8, 16, 24, 32, 40, 48, . . . ) and (9, 18, 27, 36, 45, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 9 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 8 and 9 is 72.

Explanation:

The LCM of two non-zero integers, x(8) and y(9), is the smallest positive integer m(72) that is divisible by both x(8) and y(9) without any remainder.

The methods to find the LCM of 8 and 9 are explained below.

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

LCM of 8 and 9 by Division Method

To calculate the LCM of 8 and 9 by the division method, we will divide the numbers(8, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 9.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 9. Write this prime number(2) on the left of the given numbers(8 and 9), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 9 is the product of all prime numbers on the left, i.e. LCM(8, 9) by division method = 2 × 2 × 2 × 3 × 3 = 72.

LCM of 8 and 9 by Prime Factorization

Prime factorization of 8 and 9 is (2 × 2 × 2) = 2³ and (3 × 3) = 3² respectively. LCM of 8 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² = 72.
Hence, the LCM of 8 and 9 by prime factorization is 72.

LCM of 8 and 9 by Listing Multiples

To calculate the LCM of 8 and 9 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 9 (9, 18, 27, 36, 45, . . . . )
• Step 2: The common multiples from the multiples of 8 and 9 are 72, 144, . . .
• Step 3: The smallest common multiple of 8 and 9 is 72.

∴ The least common multiple of 8 and 9 = 72.

☛ Also Check:

• LCM of 12 and 21 - 84
• LCM of 4 and 6 - 12
• LCM of 30 and 90 - 90
• LCM of 24 and 42 - 168
• LCM of 5, 6 and 8 - 120
• LCM of 36 and 81 - 324
• LCM of 108 and 144 - 432

FAQs on LCM of 8 and 9

What is the LCM of 8 and 9?

The LCM of 8 and 9 is 72. To find the LCM of 8 and 9, we need to find the multiples of 8 and 9 (multiples of 8 = 8, 16, 24, 32 . . . . 72; multiples of 9 = 9, 18, 27, 36 . . . . 72) and choose the smallest multiple that is exactly divisible by 8 and 9, i.e., 72.

If the LCM of 9 and 8 is 72, Find its GCF.

LCM(9, 8) × GCF(9, 8) = 9 × 8
Since the LCM of 9 and 8 = 72
⇒ 72 × GCF(9, 8) = 72
Therefore, the GCF (greatest common factor) = 72/72 = 1.

Which of the following is the LCM of 8 and 9? 16, 72, 15, 28

The value of LCM of 8, 9 is the smallest common multiple of 8 and 9. The number satisfying the given condition is 72.

What is the Relation Between GCF and LCM of 8, 9?

The following equation can be used to express the relation between GCF and LCM of 8 and 9, i.e. GCF × LCM = 8 × 9.

What is the Least Perfect Square Divisible by 8 and 9?

The least number divisible by 8 and 9 = LCM(8, 9)
LCM of 8 and 9 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 8 and 9 = LCM(8, 9) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.