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LCM of 7 and 9

LCM of 7 and 9 is the smallest number among all common multiples of 7 and 9. The first few multiples of 7 and 9 are (7, 14, 21, 28, 35, 42, . . . ) and (9, 18, 27, 36, 45, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 9 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 7 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 7 and 9?

Answer: LCM of 7 and 9 is 63.

Explanation:

The LCM of two non-zero integers, x(7) and y(9), is the smallest positive integer m(63) that is divisible by both x(7) and y(9) without any remainder.

Methods to Find LCM of 7 and 9

Let's look at the different methods for finding the LCM of 7 and 9.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 7 and 9 by Prime Factorization

Prime factorization of 7 and 9 is (7) = 7¹ and (3 × 3) = 3² respectively. LCM of 7 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 7¹ = 63.
Hence, the LCM of 7 and 9 by prime factorization is 63.

LCM of 7 and 9 by Listing Multiples

To calculate the LCM of 7 and 9 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, 42, . . . ) and 9 (9, 18, 27, 36, 45, . . . . )
Step 2: The common multiples from the multiples of 7 and 9 are 63, 126, . . .
Step 3: The smallest common multiple of 7 and 9 is 63.

∴ The least common multiple of 7 and 9 = 63.

LCM of 7 and 9 by Division Method

To calculate the LCM of 7 and 9 by the division method, we will divide the numbers(7, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 9.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 9. Write this prime number(3) on the left of the given numbers(7 and 9), separated as per the ladder arrangement.
Step 2: If any of the given numbers (7, 9) is a multiple of 3, divide it by 3 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 7 and 9 is the product of all prime numbers on the left, i.e. LCM(7, 9) by division method = 3 × 3 × 7 = 63.

☛ Also Check:

LCM of 7 and 9 Examples

Example 1: The product of two numbers is 63. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 63
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 63/1
Therefore, the LCM is 63.
The probable combination for the given case is LCM(7, 9) = 63.
Example 2: Verify the relationship between GCF and LCM of 7 and 9.

Solution:

The relation between GCF and LCM of 7 and 9 is given as,
LCM(7, 9) × GCF(7, 9) = Product of 7, 9
Prime factorization of 7 and 9 is given as, 7 = (7) = 7¹ and 9 = (3 × 3) = 3²
LCM(7, 9) = 63
GCF(7, 9) = 1
LHS = LCM(7, 9) × GCF(7, 9) = 63 × 1 = 63
RHS = Product of 7, 9 = 7 × 9 = 63
⇒ LHS = RHS = 63
Hence, verified.
Example 3: The GCD and LCM of two numbers are 1 and 63 respectively. If one number is 9, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 9 × b
⇒ b = (GCD × LCM)/9
⇒ b = (1 × 63)/9
⇒ b = 7
Therefore, the other number is 7.

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FAQs on LCM of 7 and 9

What is the LCM of 7 and 9?

The LCM of 7 and 9 is 63. To find the least common multiple (LCM) of 7 and 9, we need to find the multiples of 7 and 9 (multiples of 7 = 7, 14, 21, 28 . . . . 63; multiples of 9 = 9, 18, 27, 36 . . . . 63) and choose the smallest multiple that is exactly divisible by 7 and 9, i.e., 63.

What is the Least Perfect Square Divisible by 7 and 9?

The least number divisible by 7 and 9 = LCM(7, 9)
LCM of 7 and 9 = 3 × 3 × 7 [Incomplete pair(s): 7]
⇒ Least perfect square divisible by each 7 and 9 = LCM(7, 9) × 7 = 441 [Square root of 441 = √441 = ±21]
Therefore, 441 is the required number.

Which of the following is the LCM of 7 and 9? 30, 24, 15, 63

The value of LCM of 7, 9 is the smallest common multiple of 7 and 9. The number satisfying the given condition is 63.

If the LCM of 9 and 7 is 63, Find its GCF.

LCM(9, 7) × GCF(9, 7) = 9 × 7
Since the LCM of 9 and 7 = 63
⇒ 63 × GCF(9, 7) = 63
Therefore, the GCF (greatest common factor) = 63/63 = 1.

How to Find the LCM of 7 and 9 by Prime Factorization?

To find the LCM of 7 and 9 using prime factorization, we will find the prime factors, (7 = 7) and (9 = 3 × 3). LCM of 7 and 9 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 9.
⇒ LCM of 7, 9 = 3² × 7¹ = 63.

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