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LCM of 7 and 7

LCM of 7 and 7 is the smallest number among all multiples of 7. The first few multiples of 7 are (7, 14, 21, 28, 35, . . . ). There are 2 commonly used methods to find LCM of 7 and 7 - by division method, and by listing multiples.

1.	LCM of 7 and 7
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 7 and 7?

Answer: LCM of 7 and 7 is 7.

Explanation:

The LCM of non-zero integers, x(7) and y(7), is the smallest positive integer m(7) that is divisible by both x(7) and y(7) without any remainder.

Methods to Find LCM of 7 and 7

Let's look at the different methods for finding the LCM of 7 and 7.

By Division Method
By Listing Multiples

LCM of 7 and 7 by Division Method

To calculate the LCM of 7 and 7 by the division method, we will divide the numbers(7, 7) by their prime factors, as long as at least one of the numbers is evenly divisible by a prime number. The product of these divisors gives the LCM of 7 and 7.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 7. Write this prime number(7) on the left of the given numbers(7 and 7), separated as per the ladder arrangement.
Step 2: Divide the given numbers (7, 7) by 7 and write the quotient below them.
Step 3: Since only 1s are left in the last row, we can stop the division here.

The LCM of 7 and 7 by division method is given as, LCM(7, 7) = 7.

LCM of 7 and 7 by Listing Multiples

To calculate the LCM of 7 and 7 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, . . . ).
Step 3: The smallest multiple of 7 is 7.

∴ The least common multiple of 7 and 7 = 7.

☛ Also Check:

LCM of 7 and 7 Examples

Example 1: Verify the relationship between GCF and LCM of 7 and 7.

Solution:

The relation between GCF and LCM of 7 and 7 is given as,
LCM(7, 7) = 7
GCF(7, 7) = 7
LHS = LCM(7, 7) × GCF(7, 7) = 7 × 7 = 49
RHS = Product of 7, 7 = 7 × 7 = 49
⇒ LHS = RHS = 49
Hence, verified.
Example 2: The GCD and LCM of two numbers are 7 and 7 respectively. If one number is 7, find the other number.

Solution:

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

Solution:

Given: GCD = 7
product of numbers = 49
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 49/7
Therefore, the LCM is 7.
The probable combination for the given case is LCM(7, 7) = 7.

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FAQs on LCM of 7 and 7

What is the LCM of 7 and 7?

The LCM of 7 and 7 is 7. To find the least common multiple of 7 and 7, we need to find the multiples of 7(multiples of 7 = 7, 14, 21, 28, . .) and choose the smallest multiple that is exactly divisible by 7 and 7, i.e., 7.

If the LCM of 7 and 7 is 7, Find its GCF.

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

What is the Relation Between GCF and LCM of 7, 7?

The following equation can be used to express the relation between GCF and LCM of 7 and 7, i.e. GCF × LCM = 7 × 7.

What is the Least Perfect Square Divisible by 7 and 7?

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

What are the Methods to Find LCM of 7 and 7?

The commonly used methods to find the LCM of 7 and 7 are:

Division Method
Listing Multiples

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