LCM of 9 and 10
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.
1.  LCM of 9 and 10 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 9 and 10?
Answer: LCM of 9 and 10 is 90.
Explanation:
The LCM of two nonzero 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) = 3^{2} and (2 × 5) = 2^{1} × 5^{1} respectively. LCM of 9 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 5^{1} = 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
LCM of 9 and 10 Examples

Example 1: The product of two numbers is 90. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 90
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 90/1
Therefore, the LCM is 90.
The probable combination for the given case is LCM(9, 10) = 90. 
Example 2: The GCD and LCM of two numbers are 1 and 90 respectively. If one number is 10, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 10 × y
⇒ y = (GCD × LCM)/10
⇒ y = (1 × 90)/10
⇒ y = 9
Therefore, the other number is 9. 
Example 3: Find the smallest number that is divisible by 9 and 10 exactly.
Solution:
The smallest number that is divisible by 9 and 10 exactly is their LCM.
⇒ Multiples of 9 and 10: Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . .
 Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, . . . .
Therefore, the LCM of 9 and 10 is 90.
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