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LCM of 14 and 49

LCM of 14 and 49 is the smallest number among all common multiples of 14 and 49. The first few multiples of 14 and 49 are (14, 28, 42, 56, . . . ) and (49, 98, 147, 196, 245, 294, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 49 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 14 and 49
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 14 and 49?

Answer: LCM of 14 and 49 is 98.

Explanation:

The LCM of two non-zero integers, x(14) and y(49), is the smallest positive integer m(98) that is divisible by both x(14) and y(49) without any remainder.

Methods to Find LCM of 14 and 49

Let's look at the different methods for finding the LCM of 14 and 49.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 14 and 49 by Prime Factorization

Prime factorization of 14 and 49 is (2 × 7) = 2¹ × 7¹ and (7 × 7) = 7² respectively. LCM of 14 and 49 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 7² = 98.
Hence, the LCM of 14 and 49 by prime factorization is 98.

LCM of 14 and 49 by Listing Multiples

To calculate the LCM of 14 and 49 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, . . . ) and 49 (49, 98, 147, 196, 245, 294, . . . . )
Step 2: The common multiples from the multiples of 14 and 49 are 98, 196, . . .
Step 3: The smallest common multiple of 14 and 49 is 98.

∴ The least common multiple of 14 and 49 = 98.

LCM of 14 and 49 by Division Method

To calculate the LCM of 14 and 49 by the division method, we will divide the numbers(14, 49) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 49.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 49. Write this prime number(2) on the left of the given numbers(14 and 49), separated as per the ladder arrangement.
Step 2: If any of the given numbers (14, 49) 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 49 is the product of all prime numbers on the left, i.e. LCM(14, 49) by division method = 2 × 7 × 7 = 98.

☛ Also Check:

LCM of 14 and 49 Examples

Example 1: The GCD and LCM of two numbers are 7 and 98 respectively. If one number is 49, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 49 × m
⇒ m = (GCD × LCM)/49
⇒ m = (7 × 98)/49
⇒ m = 14
Therefore, the other number is 14.
Example 2: The product of two numbers is 686. If their GCD is 7, what is their LCM?

Solution:

Given: GCD = 7
product of numbers = 686
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 686/7
Therefore, the LCM is 98.
The probable combination for the given case is LCM(14, 49) = 98.
Example 3: Verify the relationship between GCF and LCM of 14 and 49.

Solution:

The relation between GCF and LCM of 14 and 49 is given as,
LCM(14, 49) × GCF(14, 49) = Product of 14, 49
Prime factorization of 14 and 49 is given as, 14 = (2 × 7) = 2¹ × 7¹ and 49 = (7 × 7) = 7²
LCM(14, 49) = 98
GCF(14, 49) = 7
LHS = LCM(14, 49) × GCF(14, 49) = 98 × 7 = 686
RHS = Product of 14, 49 = 14 × 49 = 686
⇒ LHS = RHS = 686
Hence, verified.

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FAQs on LCM of 14 and 49

What is the LCM of 14 and 49?

The LCM of 14 and 49 is 98. To find the LCM (least common multiple) of 14 and 49, we need to find the multiples of 14 and 49 (multiples of 14 = 14, 28, 42, 56 . . . . 98; multiples of 49 = 49, 98, 147, 196) and choose the smallest multiple that is exactly divisible by 14 and 49, i.e., 98.

How to Find the LCM of 14 and 49 by Prime Factorization?

To find the LCM of 14 and 49 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (49 = 7 × 7). LCM of 14 and 49 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 49.
⇒ LCM of 14, 49 = 2¹ × 7² = 98.

What is the Least Perfect Square Divisible by 14 and 49?

The least number divisible by 14 and 49 = LCM(14, 49)
LCM of 14 and 49 = 2 × 7 × 7 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 14 and 49 = LCM(14, 49) × 2 = 196 [Square root of 196 = √196 = ±14]
Therefore, 196 is the required number.

What are the Methods to Find LCM of 14 and 49?

The commonly used methods to find the LCM of 14 and 49 are:

Listing Multiples
Division Method
Prime Factorization Method

If the LCM of 49 and 14 is 98, Find its GCF.

LCM(49, 14) × GCF(49, 14) = 49 × 14
Since the LCM of 49 and 14 = 98
⇒ 98 × GCF(49, 14) = 686
Therefore, the GCF (greatest common factor) = 686/98 = 7.

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