LCM of 15 and 24
LCM of 15 and 24 is the smallest number among all common multiples of 15 and 24. The first few multiples of 15 and 24 are (15, 30, 45, 60, 75, . . . ) and (24, 48, 72, 96, 120, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 24  by division method, by prime factorization, and by listing multiples.
1.  LCM of 15 and 24 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 15 and 24?
Answer: LCM of 15 and 24 is 120.
Explanation:
The LCM of two nonzero integers, x(15) and y(24), is the smallest positive integer m(120) that is divisible by both x(15) and y(24) without any remainder.
Methods to Find LCM of 15 and 24
The methods to find the LCM of 15 and 24 are explained below.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 15 and 24 by Division Method
To calculate the LCM of 15 and 24 by the division method, we will divide the numbers(15, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 24.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 24. Write this prime number(2) on the left of the given numbers(15 and 24), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (15, 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 15 and 24 is the product of all prime numbers on the left, i.e. LCM(15, 24) by division method = 2 × 2 × 2 × 3 × 5 = 120.
LCM of 15 and 24 by Prime Factorization
Prime factorization of 15 and 24 is (3 × 5) = 3^{1} × 5^{1} and (2 × 2 × 2 × 3) = 2^{3} × 3^{1} respectively. LCM of 15 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{1} × 5^{1} = 120.
Hence, the LCM of 15 and 24 by prime factorization is 120.
LCM of 15 and 24 by Listing Multiples
To calculate the LCM of 15 and 24 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, . . . ) and 24 (24, 48, 72, 96, 120, 144, . . . . )
 Step 2: The common multiples from the multiples of 15 and 24 are 120, 240, . . .
 Step 3: The smallest common multiple of 15 and 24 is 120.
∴ The least common multiple of 15 and 24 = 120.
☛ Also Check:
 LCM of 35 and 40  280
 LCM of 34 and 51  102
 LCM of 32 and 80  160
 LCM of 32 and 64  64
 LCM of 32 and 48  96
 LCM of 32 and 40  160
 LCM of 32 and 36  288
LCM of 15 and 24 Examples

Example 1: The GCD and LCM of two numbers are 3 and 120 respectively. If one number is 15, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 15 × a
⇒ a = (GCD × LCM)/15
⇒ a = (3 × 120)/15
⇒ a = 24
Therefore, the other number is 24. 
Example 2: The product of two numbers is 360. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 360
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 360/3
Therefore, the LCM is 120.
The probable combination for the given case is LCM(15, 24) = 120. 
Example 3: Verify the relationship between GCF and LCM of 15 and 24.
Solution:
The relation between GCF and LCM of 15 and 24 is given as,
LCM(15, 24) × GCF(15, 24) = Product of 15, 24
Prime factorization of 15 and 24 is given as, 15 = (3 × 5) = 3^{1} × 5^{1} and 24 = (2 × 2 × 2 × 3) = 2^{3} × 3^{1}
LCM(15, 24) = 120
GCF(15, 24) = 3
LHS = LCM(15, 24) × GCF(15, 24) = 120 × 3 = 360
RHS = Product of 15, 24 = 15 × 24 = 360
⇒ LHS = RHS = 360
Hence, verified.
FAQs on LCM of 15 and 24
What is the LCM of 15 and 24?
The LCM of 15 and 24 is 120. To find the LCM (least common multiple) of 15 and 24, we need to find the multiples of 15 and 24 (multiples of 15 = 15, 30, 45, 60 . . . . 120; multiples of 24 = 24, 48, 72, 96 . . . . 120) and choose the smallest multiple that is exactly divisible by 15 and 24, i.e., 120.
How to Find the LCM of 15 and 24 by Prime Factorization?
To find the LCM of 15 and 24 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (24 = 2 × 2 × 2 × 3). LCM of 15 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 24.
⇒ LCM of 15, 24 = 2^{3} × 3^{1} × 5^{1} = 120.
What are the Methods to Find LCM of 15 and 24?
The commonly used methods to find the LCM of 15 and 24 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
What is the Least Perfect Square Divisible by 15 and 24?
The least number divisible by 15 and 24 = LCM(15, 24)
LCM of 15 and 24 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 15 and 24 = LCM(15, 24) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.
If the LCM of 24 and 15 is 120, Find its GCF.
LCM(24, 15) × GCF(24, 15) = 24 × 15
Since the LCM of 24 and 15 = 120
⇒ 120 × GCF(24, 15) = 360
Therefore, the GCF (greatest common factor) = 360/120 = 3.
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