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LCM of 2923 and 3239

LCM of 2923 and 3239 is the smallest number among all common multiples of 2923 and 3239. The first few multiples of 2923 and 3239 are (2923, 5846, 8769, 11692, 14615, 17538, . . . ) and (3239, 6478, 9717, 12956, 16195, 19434, 22673, . . . ) respectively. There are 3 commonly used methods to find LCM of 2923 and 3239 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 2923 and 3239
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 2923 and 3239?

Answer: LCM of 2923 and 3239 is 119843.

Explanation:

The LCM of two non-zero integers, x(2923) and y(3239), is the smallest positive integer m(119843) that is divisible by both x(2923) and y(3239) without any remainder.

Methods to Find LCM of 2923 and 3239

The methods to find the LCM of 2923 and 3239 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 2923 and 3239 by Prime Factorization

Prime factorization of 2923 and 3239 is (37 × 79) = 37¹ × 79¹ and (41 × 79) = 41¹ × 79¹ respectively. LCM of 2923 and 3239 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 37¹ × 41¹ × 79¹ = 119843.
Hence, the LCM of 2923 and 3239 by prime factorization is 119843.

LCM of 2923 and 3239 by Listing Multiples

To calculate the LCM of 2923 and 3239 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 2923 (2923, 5846, 8769, 11692, 14615, 17538, . . . ) and 3239 (3239, 6478, 9717, 12956, 16195, 19434, 22673, . . . . )
Step 2: The common multiples from the multiples of 2923 and 3239 are 119843, 239686, . . .
Step 3: The smallest common multiple of 2923 and 3239 is 119843.

∴ The least common multiple of 2923 and 3239 = 119843.

LCM of 2923 and 3239 by Division Method

To calculate the LCM of 2923 and 3239 by the division method, we will divide the numbers(2923, 3239) by their prime factors (preferably common). The product of these divisors gives the LCM of 2923 and 3239.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2923 and 3239. Write this prime number(37) on the left of the given numbers(2923 and 3239), separated as per the ladder arrangement.
Step 2: If any of the given numbers (2923, 3239) is a multiple of 37, divide it by 37 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 2923 and 3239 is the product of all prime numbers on the left, i.e. LCM(2923, 3239) by division method = 37 × 41 × 79 = 119843.

☛ Also Check:

LCM of 2923 and 3239 Examples

Example 1: The GCD and LCM of two numbers are 79 and 119843 respectively. If one number is 2923, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 2923 × y
⇒ y = (GCD × LCM)/2923
⇒ y = (79 × 119843)/2923
⇒ y = 3239
Therefore, the other number is 3239.
Example 2: Verify the relationship between GCF and LCM of 2923 and 3239.

Solution:

The relation between GCF and LCM of 2923 and 3239 is given as,
LCM(2923, 3239) × GCF(2923, 3239) = Product of 2923, 3239
Prime factorization of 2923 and 3239 is given as, 2923 = (37 × 79) = 37¹ × 79¹ and 3239 = (41 × 79) = 41¹ × 79¹
LCM(2923, 3239) = 119843
GCF(2923, 3239) = 79
LHS = LCM(2923, 3239) × GCF(2923, 3239) = 119843 × 79 = 9467597
RHS = Product of 2923, 3239 = 2923 × 3239 = 9467597
⇒ LHS = RHS = 9467597
Hence, verified.
Example 3: The product of two numbers is 9467597. If their GCD is 79, what is their LCM?

Solution:

Given: GCD = 79
product of numbers = 9467597
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 9467597/79
Therefore, the LCM is 119843.
The probable combination for the given case is LCM(2923, 3239) = 119843.

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FAQs on LCM of 2923 and 3239

What is the LCM of 2923 and 3239?

The LCM of 2923 and 3239 is 119843. To find the least common multiple (LCM) of 2923 and 3239, we need to find the multiples of 2923 and 3239 (multiples of 2923 = 2923, 5846, 8769, 11692 . . . . 119843; multiples of 3239 = 3239, 6478, 9717, 12956 . . . . 119843) and choose the smallest multiple that is exactly divisible by 2923 and 3239, i.e., 119843.

What is the Least Perfect Square Divisible by 2923 and 3239?

The least number divisible by 2923 and 3239 = LCM(2923, 3239)
LCM of 2923 and 3239 = 37 × 41 × 79 [Incomplete pair(s): 37, 41, 79]
⇒ Least perfect square divisible by each 2923 and 3239 = LCM(2923, 3239) × 37 × 41 × 79 = 14362344649 [Square root of 14362344649 = √14362344649 = ±119843]
Therefore, 14362344649 is the required number.

What is the Relation Between GCF and LCM of 2923, 3239?

The following equation can be used to express the relation between GCF and LCM of 2923 and 3239, i.e. GCF × LCM = 2923 × 3239.

If the LCM of 3239 and 2923 is 119843, Find its GCF.

LCM(3239, 2923) × GCF(3239, 2923) = 3239 × 2923
Since the LCM of 3239 and 2923 = 119843
⇒ 119843 × GCF(3239, 2923) = 9467597
Therefore, the GCF (greatest common factor) = 9467597/119843 = 79.

Which of the following is the LCM of 2923 and 3239? 15, 119843, 42, 36

The value of LCM of 2923, 3239 is the smallest common multiple of 2923 and 3239. The number satisfying the given condition is 119843.

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