LCM of 36 and 96
LCM of 36 and 96 is the smallest number among all common multiples of 36 and 96. The first few multiples of 36 and 96 are (36, 72, 108, 144, . . . ) and (96, 192, 288, 384, 480, 576, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 96  by listing multiples, by prime factorization, and by division method.
1.  LCM of 36 and 96 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 36 and 96?
Answer: LCM of 36 and 96 is 288.
Explanation:
The LCM of two nonzero integers, x(36) and y(96), is the smallest positive integer m(288) that is divisible by both x(36) and y(96) without any remainder.
Methods to Find LCM of 36 and 96
Let's look at the different methods for finding the LCM of 36 and 96.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 36 and 96 by Division Method
To calculate the LCM of 36 and 96 by the division method, we will divide the numbers(36, 96) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 96.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 96. Write this prime number(2) on the left of the given numbers(36 and 96), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (36, 96) 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 36 and 96 is the product of all prime numbers on the left, i.e. LCM(36, 96) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.
LCM of 36 and 96 by Prime Factorization
Prime factorization of 36 and 96 is (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and (2 × 2 × 2 × 2 × 2 × 3) = 2^{5} × 3^{1} respectively. LCM of 36 and 96 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{5} × 3^{2} = 288.
Hence, the LCM of 36 and 96 by prime factorization is 288.
LCM of 36 and 96 by Listing Multiples
To calculate the LCM of 36 and 96 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 36 (36, 72, 108, 144, . . . ) and 96 (96, 192, 288, 384, 480, 576, . . . . )
 Step 2: The common multiples from the multiples of 36 and 96 are 288, 576, . . .
 Step 3: The smallest common multiple of 36 and 96 is 288.
∴ The least common multiple of 36 and 96 = 288.
☛ Also Check:
 LCM of 10 and 50  50
 LCM of 148 and 185  740
 LCM of 13 and 39  39
 LCM of 12 and 18  36
 LCM of 32 and 48  96
 LCM of 16 and 20  80
 LCM of 60 and 66  660
LCM of 36 and 96 Examples

Example 1: The GCD and LCM of two numbers are 12 and 288 respectively. If one number is 96, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 96 × m
⇒ m = (GCD × LCM)/96
⇒ m = (12 × 288)/96
⇒ m = 36
Therefore, the other number is 36. 
Example 2: Find the smallest number that is divisible by 36 and 96 exactly.
Solution:
The smallest number that is divisible by 36 and 96 exactly is their LCM.
⇒ Multiples of 36 and 96: Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, . . . .
 Multiples of 96 = 96, 192, 288, 384, 480, 576, . . . .
Therefore, the LCM of 36 and 96 is 288.

Example 3: Verify the relationship between GCF and LCM of 36 and 96.
Solution:
The relation between GCF and LCM of 36 and 96 is given as,
LCM(36, 96) × GCF(36, 96) = Product of 36, 96
Prime factorization of 36 and 96 is given as, 36 = (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and 96 = (2 × 2 × 2 × 2 × 2 × 3) = 2^{5} × 3^{1}
LCM(36, 96) = 288
GCF(36, 96) = 12
LHS = LCM(36, 96) × GCF(36, 96) = 288 × 12 = 3456
RHS = Product of 36, 96 = 36 × 96 = 3456
⇒ LHS = RHS = 3456
Hence, verified.
FAQs on LCM of 36 and 96
What is the LCM of 36 and 96?
The LCM of 36 and 96 is 288. To find the LCM of 36 and 96, we need to find the multiples of 36 and 96 (multiples of 36 = 36, 72, 108, 144 . . . . 288; multiples of 96 = 96, 192, 288, 384) and choose the smallest multiple that is exactly divisible by 36 and 96, i.e., 288.
Which of the following is the LCM of 36 and 96? 21, 27, 2, 288
The value of LCM of 36, 96 is the smallest common multiple of 36 and 96. The number satisfying the given condition is 288.
If the LCM of 96 and 36 is 288, Find its GCF.
LCM(96, 36) × GCF(96, 36) = 96 × 36
Since the LCM of 96 and 36 = 288
⇒ 288 × GCF(96, 36) = 3456
Therefore, the GCF (greatest common factor) = 3456/288 = 12.
How to Find the LCM of 36 and 96 by Prime Factorization?
To find the LCM of 36 and 96 using prime factorization, we will find the prime factors, (36 = 2 × 2 × 3 × 3) and (96 = 2 × 2 × 2 × 2 × 2 × 3). LCM of 36 and 96 is the product of prime factors raised to their respective highest exponent among the numbers 36 and 96.
⇒ LCM of 36, 96 = 2^{5} × 3^{2} = 288.
What is the Relation Between GCF and LCM of 36, 96?
The following equation can be used to express the relation between GCF and LCM of 36 and 96, i.e. GCF × LCM = 36 × 96.
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