LCM of 9 and 10 - How to Find LCM of 9, 10? (2024)

LCM of 9 and 10 is the smallest number among all common multiples of 9 and 10. The first few multiples of 9 and 10 are (9, 18, 27, 36, 45, 54, 63, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 10 - by prime factorization, by division method, and by listing multiples.

What is the LCM of 9 and 10?

Answer: LCM of 9 and 10 is 90.

Explanation:

The LCM of two non-zero integers, x(9) and y(10), is the smallest positive integer m(90) that is divisible by both x(9) and y(10) without any remainder.

Methods to Find LCM of 9 and 10

Let's look at the different methods for finding the LCM of 9 and 10.

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

LCM of 9 and 10 by Prime Factorization

Prime factorization of 9 and 10 is (3 × 3) = 3² and (2 × 5) = 2¹ × 5¹ respectively. LCM of 9 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ = 90.
Hence, the LCM of 9 and 10 by prime factorization is 90.

LCM of 9 and 10 by Listing Multiples

To calculate the LCM of 9 and 10 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 10 (10, 20, 30, 40, . . . . )
• Step 2: The common multiples from the multiples of 9 and 10 are 90, 180, . . .
• Step 3: The smallest common multiple of 9 and 10 is 90.

∴ The least common multiple of 9 and 10 = 90.

LCM of 9 and 10 by Division Method

To calculate the LCM of 9 and 10 by the division method, we will divide the numbers(9, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 10.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 10. Write this prime number(2) on the left of the given numbers(9 and 10), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 10) 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 10 is the product of all prime numbers on the left, i.e. LCM(9, 10) by division method = 2 × 3 × 3 × 5 = 90.

☛ Also Check:

• LCM of 35 and 60 - 420
• LCM of 72 and 96 - 288
• LCM of 16 and 36 - 144
• LCM of 34 and 51 - 102
• LCM of 12 and 40 - 120
• LCM of 90 and 105 - 630
• LCM of 3 and 3 - 3

FAQs on LCM of 9 and 10

What is the LCM of 9 and 10?

The LCM of 9 and 10 is 90. To find the LCM of 9 and 10, we need to find the multiples of 9 and 10 (multiples of 9 = 9, 18, 27, 36 . . . . 90; multiples of 10 = 10, 20, 30, 40 . . . . 90) and choose the smallest multiple that is exactly divisible by 9 and 10, i.e., 90.

If the LCM of 10 and 9 is 90, Find its GCF.

LCM(10, 9) × GCF(10, 9) = 10 × 9
Since the LCM of 10 and 9 = 90
⇒ 90 × GCF(10, 9) = 90
Therefore, the greatest common factor (GCF) = 90/90 = 1.

What is the Relation Between GCF and LCM of 9, 10?

The following equation can be used to express the relation between GCF and LCM of 9 and 10, i.e. GCF × LCM = 9 × 10.

What is the Least Perfect Square Divisible by 9 and 10?

The least number divisible by 9 and 10 = LCM(9, 10)
LCM of 9 and 10 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 9 and 10 = LCM(9, 10) × 2 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

What are the Methods to Find LCM of 9 and 10?

The commonly used methods to find the LCM of 9 and 10 are:

• Division Method
• Listing Multiples
• Prime Factorization Method