LCM of 9 and 24
LCM of 9 and 24 is the smallest number among all common multiples of 9 and 24. The first few multiples of 9 and 24 are (9, 18, 27, 36, 45, 54, 63, . . . ) and (24, 48, 72, 96, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 24  by prime factorization, by division method, and by listing multiples.
1.  LCM of 9 and 24 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 9 and 24?
Answer: LCM of 9 and 24 is 72.
Explanation:
The LCM of two nonzero integers, x(9) and y(24), is the smallest positive integer m(72) that is divisible by both x(9) and y(24) without any remainder.
Methods to Find LCM of 9 and 24
Let's look at the different methods for finding the LCM of 9 and 24.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 9 and 24 by Division Method
To calculate the LCM of 9 and 24 by the division method, we will divide the numbers(9, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 24.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 24. Write this prime number(2) on the left of the given numbers(9 and 24), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (9, 24) 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 24 is the product of all prime numbers on the left, i.e. LCM(9, 24) by division method = 2 × 2 × 2 × 3 × 3 = 72.
LCM of 9 and 24 by Listing Multiples
To calculate the LCM of 9 and 24 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 24 (24, 48, 72, 96, 120, . . . . )
 Step 2: The common multiples from the multiples of 9 and 24 are 72, 144, . . .
 Step 3: The smallest common multiple of 9 and 24 is 72.
∴ The least common multiple of 9 and 24 = 72.
LCM of 9 and 24 by Prime Factorization
Prime factorization of 9 and 24 is (3 × 3) = 3^{2} and (2 × 2 × 2 × 3) = 2^{3} × 3^{1} respectively. LCM of 9 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{2} = 72.
Hence, the LCM of 9 and 24 by prime factorization is 72.
☛ Also Check:
 LCM of 30 and 42  210
 LCM of 64 and 80  320
 LCM of 2 and 2  2
 LCM of 45 and 75  225
 LCM of 8 and 64  64
 LCM of 26 and 39  78
 LCM of 5 and 8  40
LCM of 9 and 24 Examples

Example 1: Verify the relationship between GCF and LCM of 9 and 24.
Solution:
The relation between GCF and LCM of 9 and 24 is given as,
LCM(9, 24) × GCF(9, 24) = Product of 9, 24
Prime factorization of 9 and 24 is given as, 9 = (3 × 3) = 3^{2} and 24 = (2 × 2 × 2 × 3) = 2^{3} × 3^{1}
LCM(9, 24) = 72
GCF(9, 24) = 3
LHS = LCM(9, 24) × GCF(9, 24) = 72 × 3 = 216
RHS = Product of 9, 24 = 9 × 24 = 216
⇒ LHS = RHS = 216
Hence, verified. 
Example 2: Find the smallest number that is divisible by 9 and 24 exactly.
Solution:
The smallest number that is divisible by 9 and 24 exactly is their LCM.
⇒ Multiples of 9 and 24: Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, . . . .
 Multiples of 24 = 24, 48, 72, 96, 120, 144, . . . .
Therefore, the LCM of 9 and 24 is 72.

Example 3: The GCD and LCM of two numbers are 3 and 72 respectively. If one number is 9, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 9 × z
⇒ z = (GCD × LCM)/9
⇒ z = (3 × 72)/9
⇒ z = 24
Therefore, the other number is 24.
FAQs on LCM of 9 and 24
What is the LCM of 9 and 24?
The LCM of 9 and 24 is 72. To find the least common multiple of 9 and 24, we need to find the multiples of 9 and 24 (multiples of 9 = 9, 18, 27, 36 . . . . 72; multiples of 24 = 24, 48, 72, 96) and choose the smallest multiple that is exactly divisible by 9 and 24, i.e., 72.
What are the Methods to Find LCM of 9 and 24?
The commonly used methods to find the LCM of 9 and 24 are:
 Prime Factorization Method
 Listing Multiples
 Division Method
If the LCM of 24 and 9 is 72, Find its GCF.
LCM(24, 9) × GCF(24, 9) = 24 × 9
Since the LCM of 24 and 9 = 72
⇒ 72 × GCF(24, 9) = 216
Therefore, the greatest common factor = 216/72 = 3.
What is the Least Perfect Square Divisible by 9 and 24?
The least number divisible by 9 and 24 = LCM(9, 24)
LCM of 9 and 24 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 9 and 24 = LCM(9, 24) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.
How to Find the LCM of 9 and 24 by Prime Factorization?
To find the LCM of 9 and 24 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (24 = 2 × 2 × 2 × 3). LCM of 9 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 24.
⇒ LCM of 9, 24 = 2^{3} × 3^{2} = 72.
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