LCM of 64 and 72
LCM of 64 and 72 is the smallest number among all common multiples of 64 and 72. The first few multiples of 64 and 72 are (64, 128, 192, 256, . . . ) and (72, 144, 216, 288, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 64 and 72  by prime factorization, by listing multiples, and by division method.
1.  LCM of 64 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 64 and 72?
Answer: LCM of 64 and 72 is 576.
Explanation:
The LCM of two nonzero integers, x(64) and y(72), is the smallest positive integer m(576) that is divisible by both x(64) and y(72) without any remainder.
Methods to Find LCM of 64 and 72
Let's look at the different methods for finding the LCM of 64 and 72.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 64 and 72 by Listing Multiples
To calculate the LCM of 64 and 72 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 64 (64, 128, 192, 256, . . . ) and 72 (72, 144, 216, 288, 360, . . . . )
 Step 2: The common multiples from the multiples of 64 and 72 are 576, 1152, . . .
 Step 3: The smallest common multiple of 64 and 72 is 576.
∴ The least common multiple of 64 and 72 = 576.
LCM of 64 and 72 by Division Method
To calculate the LCM of 64 and 72 by the division method, we will divide the numbers(64, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 64 and 72.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 64 and 72. Write this prime number(2) on the left of the given numbers(64 and 72), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (64, 72) 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 64 and 72 is the product of all prime numbers on the left, i.e. LCM(64, 72) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 = 576.
LCM of 64 and 72 by Prime Factorization
Prime factorization of 64 and 72 is (2 × 2 × 2 × 2 × 2 × 2) = 2^{6} and (2 × 2 × 2 × 3 × 3) = 2^{3} × 3^{2} respectively. LCM of 64 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{6} × 3^{2} = 576.
Hence, the LCM of 64 and 72 by prime factorization is 576.
☛ Also Check:
 LCM of 75 and 100  300
 LCM of 3, 4, 5 and 6  60
 LCM of 4 and 14  28
 LCM of 3, 4 and 9  36
 LCM of 17 and 34  34
 LCM of 16 and 64  64
 LCM of 16 and 60  240
LCM of 64 and 72 Examples

Example 1: Find the smallest number that is divisible by 64 and 72 exactly.
Solution:
The smallest number that is divisible by 64 and 72 exactly is their LCM.
⇒ Multiples of 64 and 72: Multiples of 64 = 64, 128, 192, 256, 320, 384, 448, 512, 576, . . . .
 Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, 576, . . . .
Therefore, the LCM of 64 and 72 is 576.

Example 2: The product of two numbers is 4608. If their GCD is 8, what is their LCM?
Solution:
Given: GCD = 8
product of numbers = 4608
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 4608/8
Therefore, the LCM is 576.
The probable combination for the given case is LCM(64, 72) = 576. 
Example 3: The GCD and LCM of two numbers are 8 and 576 respectively. If one number is 72, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 72 × a
⇒ a = (GCD × LCM)/72
⇒ a = (8 × 576)/72
⇒ a = 64
Therefore, the other number is 64.
FAQs on LCM of 64 and 72
What is the LCM of 64 and 72?
The LCM of 64 and 72 is 576. To find the LCM of 64 and 72, we need to find the multiples of 64 and 72 (multiples of 64 = 64, 128, 192, 256 . . . . 576; multiples of 72 = 72, 144, 216, 288 . . . . 576) and choose the smallest multiple that is exactly divisible by 64 and 72, i.e., 576.
If the LCM of 72 and 64 is 576, Find its GCF.
LCM(72, 64) × GCF(72, 64) = 72 × 64
Since the LCM of 72 and 64 = 576
⇒ 576 × GCF(72, 64) = 4608
Therefore, the greatest common factor = 4608/576 = 8.
What is the Relation Between GCF and LCM of 64, 72?
The following equation can be used to express the relation between GCF and LCM of 64 and 72, i.e. GCF × LCM = 64 × 72.
What is the Least Perfect Square Divisible by 64 and 72?
The least number divisible by 64 and 72 = LCM(64, 72)
LCM of 64 and 72 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 64 and 72 = 576 [Square root of 576 = √576 = ±24]
Therefore, 576 is the required number.
How to Find the LCM of 64 and 72 by Prime Factorization?
To find the LCM of 64 and 72 using prime factorization, we will find the prime factors, (64 = 2 × 2 × 2 × 2 × 2 × 2) and (72 = 2 × 2 × 2 × 3 × 3). LCM of 64 and 72 is the product of prime factors raised to their respective highest exponent among the numbers 64 and 72.
⇒ LCM of 64, 72 = 2^{6} × 3^{2} = 576.
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