LCM of 56 and 98
LCM of 56 and 98 is the smallest number among all common multiples of 56 and 98. The first few multiples of 56 and 98 are (56, 112, 168, 224, 280, . . . ) and (98, 196, 294, 392, 490, 588, 686, . . . ) respectively. There are 3 commonly used methods to find LCM of 56 and 98  by division method, by prime factorization, and by listing multiples.
1.  LCM of 56 and 98 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 56 and 98?
Answer: LCM of 56 and 98 is 392.
Explanation:
The LCM of two nonzero integers, x(56) and y(98), is the smallest positive integer m(392) that is divisible by both x(56) and y(98) without any remainder.
Methods to Find LCM of 56 and 98
The methods to find the LCM of 56 and 98 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 56 and 98 by Division Method
To calculate the LCM of 56 and 98 by the division method, we will divide the numbers(56, 98) by their prime factors (preferably common). The product of these divisors gives the LCM of 56 and 98.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 56 and 98. Write this prime number(2) on the left of the given numbers(56 and 98), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (56, 98) 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 98 is the product of all prime numbers on the left, i.e. LCM(56, 98) by division method = 2 × 2 × 2 × 7 × 7 = 392.
LCM of 56 and 98 by Listing Multiples
To calculate the LCM of 56 and 98 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, . . . ) and 98 (98, 196, 294, 392, 490, 588, 686, . . . . )
 Step 2: The common multiples from the multiples of 56 and 98 are 392, 784, . . .
 Step 3: The smallest common multiple of 56 and 98 is 392.
∴ The least common multiple of 56 and 98 = 392.
LCM of 56 and 98 by Prime Factorization
Prime factorization of 56 and 98 is (2 × 2 × 2 × 7) = 2^{3} × 7^{1} and (2 × 7 × 7) = 2^{1} × 7^{2} respectively. LCM of 56 and 98 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 7^{2} = 392.
Hence, the LCM of 56 and 98 by prime factorization is 392.
☛ Also Check:
 LCM of 24 and 45  360
 LCM of 28 and 42  84
 LCM of 12, 15, 20 and 54  540
 LCM of 16, 24 and 40  240
 LCM of 8, 9 and 12  72
 LCM of 7 and 13  91
 LCM of 120 and 150  600
LCM of 56 and 98 Examples

Example 1: Find the smallest number that is divisible by 56 and 98 exactly.
Solution:
The smallest number that is divisible by 56 and 98 exactly is their LCM.
⇒ Multiples of 56 and 98: Multiples of 56 = 56, 112, 168, 224, 280, 336, 392, . . . .
 Multiples of 98 = 98, 196, 294, 392, 490, 588, . . . .
Therefore, the LCM of 56 and 98 is 392.

Example 2: The GCD and LCM of two numbers are 14 and 392 respectively. If one number is 98, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 98 × y
⇒ y = (GCD × LCM)/98
⇒ y = (14 × 392)/98
⇒ y = 56
Therefore, the other number is 56. 
Example 3: Verify the relationship between GCF and LCM of 56 and 98.
Solution:
The relation between GCF and LCM of 56 and 98 is given as,
LCM(56, 98) × GCF(56, 98) = Product of 56, 98
Prime factorization of 56 and 98 is given as, 56 = (2 × 2 × 2 × 7) = 2^{3} × 7^{1} and 98 = (2 × 7 × 7) = 2^{1} × 7^{2}
LCM(56, 98) = 392
GCF(56, 98) = 14
LHS = LCM(56, 98) × GCF(56, 98) = 392 × 14 = 5488
RHS = Product of 56, 98 = 56 × 98 = 5488
⇒ LHS = RHS = 5488
Hence, verified.
FAQs on LCM of 56 and 98
What is the LCM of 56 and 98?
The LCM of 56 and 98 is 392. To find the least common multiple (LCM) of 56 and 98, we need to find the multiples of 56 and 98 (multiples of 56 = 56, 112, 168, 224 . . . . 392; multiples of 98 = 98, 196, 294, 392) and choose the smallest multiple that is exactly divisible by 56 and 98, i.e., 392.
If the LCM of 98 and 56 is 392, Find its GCF.
LCM(98, 56) × GCF(98, 56) = 98 × 56
Since the LCM of 98 and 56 = 392
⇒ 392 × GCF(98, 56) = 5488
Therefore, the GCF = 5488/392 = 14.
What is the Least Perfect Square Divisible by 56 and 98?
The least number divisible by 56 and 98 = LCM(56, 98)
LCM of 56 and 98 = 2 × 2 × 2 × 7 × 7 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 56 and 98 = LCM(56, 98) × 2 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.
What are the Methods to Find LCM of 56 and 98?
The commonly used methods to find the LCM of 56 and 98 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
What is the Relation Between GCF and LCM of 56, 98?
The following equation can be used to express the relation between GCF and LCM of 56 and 98, i.e. GCF × LCM = 56 × 98.
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