LCM of 36 and 48
LCM of 36 and 48 is the smallest number among all common multiples of 36 and 48. The first few multiples of 36 and 48 are (36, 72, 108, 144, 180, 216, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 48  by listing multiples, by prime factorization, and by division method.
1.  LCM of 36 and 48 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 36 and 48?
Answer: LCM of 36 and 48 is 144.
Explanation:
The LCM of two nonzero integers, x(36) and y(48), is the smallest positive integer m(144) that is divisible by both x(36) and y(48) without any remainder.
Methods to Find LCM of 36 and 48
The methods to find the LCM of 36 and 48 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 36 and 48 by Division Method
To calculate the LCM of 36 and 48 by the division method, we will divide the numbers(36, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 48.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 48. Write this prime number(2) on the left of the given numbers(36 and 48), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (36, 48) 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 48 is the product of all prime numbers on the left, i.e. LCM(36, 48) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.
LCM of 36 and 48 by Listing Multiples
To calculate the LCM of 36 and 48 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, 180, 216, . . . ) and 48 (48, 96, 144, 192, 240, 288, . . . . )
 Step 2: The common multiples from the multiples of 36 and 48 are 144, 288, . . .
 Step 3: The smallest common multiple of 36 and 48 is 144.
∴ The least common multiple of 36 and 48 = 144.
LCM of 36 and 48 by Prime Factorization
Prime factorization of 36 and 48 is (2 × 2 × 3 × 3) = 2^{2} × 3^{2} and (2 × 2 × 2 × 2 × 3) = 2^{4} × 3^{1} respectively. LCM of 36 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{2} = 144.
Hence, the LCM of 36 and 48 by prime factorization is 144.
☛ Also Check:
 LCM of 3, 4 and 5  60
 LCM of 36, 54 and 72  216
 LCM of 14 and 18  126
 LCM of 4, 9 and 10  180
 LCM of 9 and 21  63
 LCM of 10 and 15  30
 LCM of 63 and 21  63
LCM of 36 and 48 Examples

Example 1: The GCD and LCM of two numbers are 12 and 144 respectively. If one number is 48, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 48 × b
⇒ b = (GCD × LCM)/48
⇒ b = (12 × 144)/48
⇒ b = 36
Therefore, the other number is 36. 
Example 2: Find the smallest number that is divisible by 36 and 48 exactly.
Solution:
The smallest number that is divisible by 36 and 48 exactly is their LCM.
⇒ Multiples of 36 and 48: Multiples of 36 = 36, 72, 108, 144, 180, . . . .
 Multiples of 48 = 48, 96, 144, 192, 240, . . . .
Therefore, the LCM of 36 and 48 is 144.

Example 3: The product of two numbers is 1728. If their GCD is 12, what is their LCM?
Solution:
Given: GCD = 12
product of numbers = 1728
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1728/12
Therefore, the LCM is 144.
The probable combination for the given case is LCM(36, 48) = 144.
FAQs on LCM of 36 and 48
What is the LCM of 36 and 48?
The LCM of 36 and 48 is 144. To find the least common multiple of 36 and 48, we need to find the multiples of 36 and 48 (multiples of 36 = 36, 72, 108, 144; multiples of 48 = 48, 96, 144, 192) and choose the smallest multiple that is exactly divisible by 36 and 48, i.e., 144.
If the LCM of 48 and 36 is 144, Find its GCF.
LCM(48, 36) × GCF(48, 36) = 48 × 36
Since the LCM of 48 and 36 = 144
⇒ 144 × GCF(48, 36) = 1728
Therefore, the greatest common factor = 1728/144 = 12.
Which of the following is the LCM of 36 and 48? 10, 144, 21, 16
The value of LCM of 36, 48 is the smallest common multiple of 36 and 48. The number satisfying the given condition is 144.
What is the Relation Between GCF and LCM of 36, 48?
The following equation can be used to express the relation between GCF and LCM of 36 and 48, i.e. GCF × LCM = 36 × 48.
What is the Least Perfect Square Divisible by 36 and 48?
The least number divisible by 36 and 48 = LCM(36, 48)
LCM of 36 and 48 = 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 36 and 48 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.
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