LCM of 14 and 56
LCM of 14 and 56 is the smallest number among all common multiples of 14 and 56. The first few multiples of 14 and 56 are (14, 28, 42, 56, 70, 84, . . . ) and (56, 112, 168, 224, 280, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 56  by listing multiples, by division method, and by prime factorization.
1.  LCM of 14 and 56 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 56?
Answer: LCM of 14 and 56 is 56.
Explanation:
The LCM of two nonzero integers, x(14) and y(56), is the smallest positive integer m(56) that is divisible by both x(14) and y(56) without any remainder.
Methods to Find LCM of 14 and 56
Let's look at the different methods for finding the LCM of 14 and 56.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 14 and 56 by Listing Multiples
To calculate the LCM of 14 and 56 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 14 (14, 28, 42, 56, 70, 84, . . . ) and 56 (56, 112, 168, 224, 280, . . . . )
 Step 2: The common multiples from the multiples of 14 and 56 are 56, 112, . . .
 Step 3: The smallest common multiple of 14 and 56 is 56.
∴ The least common multiple of 14 and 56 = 56.
LCM of 14 and 56 by Division Method
To calculate the LCM of 14 and 56 by the division method, we will divide the numbers(14, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 56.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 56. Write this prime number(2) on the left of the given numbers(14 and 56), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 56) 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 14 and 56 is the product of all prime numbers on the left, i.e. LCM(14, 56) by division method = 2 × 2 × 2 × 7 = 56.
LCM of 14 and 56 by Prime Factorization
Prime factorization of 14 and 56 is (2 × 7) = 2^{1} × 7^{1} and (2 × 2 × 2 × 7) = 2^{3} × 7^{1} respectively. LCM of 14 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 7^{1} = 56.
Hence, the LCM of 14 and 56 by prime factorization is 56.
☛ Also Check:
 LCM of 6 and 12  12
 LCM of 6 and 11  66
 LCM of 6 and 10  30
 LCM of 56 and 98  392
 LCM of 56 and 84  168
 LCM of 56 and 72  504
 LCM of 56 and 70  280
LCM of 14 and 56 Examples

Example 1: Verify the relationship between GCF and LCM of 14 and 56.
Solution:
The relation between GCF and LCM of 14 and 56 is given as,
LCM(14, 56) × GCF(14, 56) = Product of 14, 56
Prime factorization of 14 and 56 is given as, 14 = (2 × 7) = 2^{1} × 7^{1} and 56 = (2 × 2 × 2 × 7) = 2^{3} × 7^{1}
LCM(14, 56) = 56
GCF(14, 56) = 14
LHS = LCM(14, 56) × GCF(14, 56) = 56 × 14 = 784
RHS = Product of 14, 56 = 14 × 56 = 784
⇒ LHS = RHS = 784
Hence, verified. 
Example 2: Find the smallest number that is divisible by 14 and 56 exactly.
Solution:
The smallest number that is divisible by 14 and 56 exactly is their LCM.
⇒ Multiples of 14 and 56: Multiples of 14 = 14, 28, 42, 56, 70, 84, . . . .
 Multiples of 56 = 56, 112, 168, 224, 280, 336, . . . .
Therefore, the LCM of 14 and 56 is 56.

Example 3: The GCD and LCM of two numbers are 14 and 56 respectively. If one number is 56, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 56 × y
⇒ y = (GCD × LCM)/56
⇒ y = (14 × 56)/56
⇒ y = 14
Therefore, the other number is 14.
FAQs on LCM of 14 and 56
What is the LCM of 14 and 56?
The LCM of 14 and 56 is 56. To find the LCM (least common multiple) of 14 and 56, we need to find the multiples of 14 and 56 (multiples of 14 = 14, 28, 42, 56; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 14 and 56, i.e., 56.
What is the Least Perfect Square Divisible by 14 and 56?
The least number divisible by 14 and 56 = LCM(14, 56)
LCM of 14 and 56 = 2 × 2 × 2 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 14 and 56 = LCM(14, 56) × 2 × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.
What is the Relation Between GCF and LCM of 14, 56?
The following equation can be used to express the relation between GCF and LCM of 14 and 56, i.e. GCF × LCM = 14 × 56.
Which of the following is the LCM of 14 and 56? 15, 11, 56, 3
The value of LCM of 14, 56 is the smallest common multiple of 14 and 56. The number satisfying the given condition is 56.
If the LCM of 56 and 14 is 56, Find its GCF.
LCM(56, 14) × GCF(56, 14) = 56 × 14
Since the LCM of 56 and 14 = 56
⇒ 56 × GCF(56, 14) = 784
Therefore, the GCF = 784/56 = 14.
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