LCM of 56 and 96
LCM of 56 and 96 is the smallest number among all common multiples of 56 and 96. The first few multiples of 56 and 96 are (56, 112, 168, 224, 280, 336, . . . ) and (96, 192, 288, 384, 480, 576, . . . ) respectively. There are 3 commonly used methods to find LCM of 56 and 96  by prime factorization, by division method, and by listing multiples.
1.  LCM of 56 and 96 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 56 and 96?
Answer: LCM of 56 and 96 is 672.
Explanation:
The LCM of two nonzero integers, x(56) and y(96), is the smallest positive integer m(672) that is divisible by both x(56) and y(96) without any remainder.
Methods to Find LCM of 56 and 96
The methods to find the LCM of 56 and 96 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 56 and 96 by Prime Factorization
Prime factorization of 56 and 96 is (2 × 2 × 2 × 7) = 2^{3} × 7^{1} and (2 × 2 × 2 × 2 × 2 × 3) = 2^{5} × 3^{1} respectively. LCM of 56 and 96 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{5} × 3^{1} × 7^{1} = 672.
Hence, the LCM of 56 and 96 by prime factorization is 672.
LCM of 56 and 96 by Division Method
To calculate the LCM of 56 and 96 by the division method, we will divide the numbers(56, 96) by their prime factors (preferably common). The product of these divisors gives the LCM of 56 and 96.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 56 and 96. Write this prime number(2) on the left of the given numbers(56 and 96), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (56, 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 56 and 96 is the product of all prime numbers on the left, i.e. LCM(56, 96) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 7 = 672.
LCM of 56 and 96 by Listing Multiples
To calculate the LCM of 56 and 96 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 56 (56, 112, 168, 224, 280, 336, . . . ) and 96 (96, 192, 288, 384, 480, 576, . . . . )
 Step 2: The common multiples from the multiples of 56 and 96 are 672, 1344, . . .
 Step 3: The smallest common multiple of 56 and 96 is 672.
∴ The least common multiple of 56 and 96 = 672.
☛ Also Check:
 LCM of 8, 15 and 20  120
 LCM of 24 and 42  168
 LCM of 148 and 185  740
 LCM of 9 and 13  117
 LCM of 84, 90 and 120  2520
 LCM of 10 and 20  20
 LCM of 20 and 25  100
LCM of 56 and 96 Examples

Example 1: Verify the relationship between GCF and LCM of 56 and 96.
Solution:
The relation between GCF and LCM of 56 and 96 is given as,
LCM(56, 96) × GCF(56, 96) = Product of 56, 96
Prime factorization of 56 and 96 is given as, 56 = (2 × 2 × 2 × 7) = 2^{3} × 7^{1} and 96 = (2 × 2 × 2 × 2 × 2 × 3) = 2^{5} × 3^{1}
LCM(56, 96) = 672
GCF(56, 96) = 8
LHS = LCM(56, 96) × GCF(56, 96) = 672 × 8 = 5376
RHS = Product of 56, 96 = 56 × 96 = 5376
⇒ LHS = RHS = 5376
Hence, verified. 
Example 2: The product of two numbers is 5376. If their GCD is 8, what is their LCM?
Solution:
Given: GCD = 8
product of numbers = 5376
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 5376/8
Therefore, the LCM is 672.
The probable combination for the given case is LCM(56, 96) = 672. 
Example 3: Find the smallest number that is divisible by 56 and 96 exactly.
Solution:
The smallest number that is divisible by 56 and 96 exactly is their LCM.
⇒ Multiples of 56 and 96: Multiples of 56 = 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, . . . .
 Multiples of 96 = 96, 192, 288, 384, 480, 576, 672, . . . .
Therefore, the LCM of 56 and 96 is 672.
FAQs on LCM of 56 and 96
What is the LCM of 56 and 96?
The LCM of 56 and 96 is 672. To find the LCM (least common multiple) of 56 and 96, we need to find the multiples of 56 and 96 (multiples of 56 = 56, 112, 168, 224 . . . . 672; multiples of 96 = 96, 192, 288, 384 . . . . 672) and choose the smallest multiple that is exactly divisible by 56 and 96, i.e., 672.
What is the Least Perfect Square Divisible by 56 and 96?
The least number divisible by 56 and 96 = LCM(56, 96)
LCM of 56 and 96 = 2 × 2 × 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 56 and 96 = LCM(56, 96) × 2 × 3 × 7 = 28224 [Square root of 28224 = √28224 = ±168]
Therefore, 28224 is the required number.
What is the Relation Between GCF and LCM of 56, 96?
The following equation can be used to express the relation between GCF and LCM of 56 and 96, i.e. GCF × LCM = 56 × 96.
If the LCM of 96 and 56 is 672, Find its GCF.
LCM(96, 56) × GCF(96, 56) = 96 × 56
Since the LCM of 96 and 56 = 672
⇒ 672 × GCF(96, 56) = 5376
Therefore, the greatest common factor = 5376/672 = 8.
How to Find the LCM of 56 and 96 by Prime Factorization?
To find the LCM of 56 and 96 using prime factorization, we will find the prime factors, (56 = 2 × 2 × 2 × 7) and (96 = 2 × 2 × 2 × 2 × 2 × 3). LCM of 56 and 96 is the product of prime factors raised to their respective highest exponent among the numbers 56 and 96.
⇒ LCM of 56, 96 = 2^{5} × 3^{1} × 7^{1} = 672.
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