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LCM of 2601 and 2616

LCM of 2601 and 2616 is the smallest number among all common multiples of 2601 and 2616. The first few multiples of 2601 and 2616 are (2601, 5202, 7803, 10404, 13005, 15606, . . . ) and (2616, 5232, 7848, 10464, . . . ) respectively. There are 3 commonly used methods to find LCM of 2601 and 2616 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 2601 and 2616
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 2601 and 2616?

Answer: LCM of 2601 and 2616 is 2268072.

Explanation:

The LCM of two non-zero integers, x(2601) and y(2616), is the smallest positive integer m(2268072) that is divisible by both x(2601) and y(2616) without any remainder.

Methods to Find LCM of 2601 and 2616

Let's look at the different methods for finding the LCM of 2601 and 2616.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 2601 and 2616 by Division Method

To calculate the LCM of 2601 and 2616 by the division method, we will divide the numbers(2601, 2616) by their prime factors (preferably common). The product of these divisors gives the LCM of 2601 and 2616.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2601 and 2616. Write this prime number(2) on the left of the given numbers(2601 and 2616), separated as per the ladder arrangement.
Step 2: If any of the given numbers (2601, 2616) 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 2601 and 2616 is the product of all prime numbers on the left, i.e. LCM(2601, 2616) by division method = 2 × 2 × 2 × 3 × 3 × 17 × 17 × 109 = 2268072.

LCM of 2601 and 2616 by Prime Factorization

Prime factorization of 2601 and 2616 is (3 × 3 × 17 × 17) = 3² × 17² and (2 × 2 × 2 × 3 × 109) = 2³ × 3¹ × 109¹ respectively. LCM of 2601 and 2616 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² × 17² × 109¹ = 2268072.
Hence, the LCM of 2601 and 2616 by prime factorization is 2268072.

LCM of 2601 and 2616 by Listing Multiples

To calculate the LCM of 2601 and 2616 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 2601 (2601, 5202, 7803, 10404, 13005, 15606, . . . ) and 2616 (2616, 5232, 7848, 10464, . . . . )
Step 2: The common multiples from the multiples of 2601 and 2616 are 2268072, 4536144, . . .
Step 3: The smallest common multiple of 2601 and 2616 is 2268072.

∴ The least common multiple of 2601 and 2616 = 2268072.

☛ Also Check:

LCM of 2601 and 2616 Examples

Example 1: The product of two numbers is 6804216. If their GCD is 3, what is their LCM?

Solution:

Given: GCD = 3
product of numbers = 6804216
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 6804216/3
Therefore, the LCM is 2268072.
The probable combination for the given case is LCM(2601, 2616) = 2268072.
Example 2: Verify the relationship between GCF and LCM of 2601 and 2616.

Solution:

The relation between GCF and LCM of 2601 and 2616 is given as,
LCM(2601, 2616) × GCF(2601, 2616) = Product of 2601, 2616
Prime factorization of 2601 and 2616 is given as, 2601 = (3 × 3 × 17 × 17) = 3² × 17² and 2616 = (2 × 2 × 2 × 3 × 109) = 2³ × 3¹ × 109¹
LCM(2601, 2616) = 2268072
GCF(2601, 2616) = 3
LHS = LCM(2601, 2616) × GCF(2601, 2616) = 2268072 × 3 = 6804216
RHS = Product of 2601, 2616 = 2601 × 2616 = 6804216
⇒ LHS = RHS = 6804216
Hence, verified.
Example 3: Find the smallest number that is divisible by 2601 and 2616 exactly.

Solution:

The value of LCM(2601, 2616) will be the smallest number that is exactly divisible by 2601 and 2616.
⇒ Multiples of 2601 and 2616:
- Multiples of 2601 = 2601, 5202, 7803, 10404, 13005, 15606, 18207, 20808, 23409, 26010, . . . ., 2257668, 2260269, 2262870, 2265471, 2268072, . . . .
- Multiples of 2616 = 2616, 5232, 7848, 10464, 13080, 15696, 18312, 20928, 23544, 26160, . . . ., 2260224, 2262840, 2265456, 2268072, . . . .
Therefore, the LCM of 2601 and 2616 is 2268072.

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FAQs on LCM of 2601 and 2616

What is the LCM of 2601 and 2616?

The LCM of 2601 and 2616 is 2268072. To find the LCM of 2601 and 2616, we need to find the multiples of 2601 and 2616 (multiples of 2601 = 2601, 5202, 7803, 10404 . . . . 2268072; multiples of 2616 = 2616, 5232, 7848, 10464 . . . . 2268072) and choose the smallest multiple that is exactly divisible by 2601 and 2616, i.e., 2268072.

Which of the following is the LCM of 2601 and 2616? 2268072, 18, 27, 45

The value of LCM of 2601, 2616 is the smallest common multiple of 2601 and 2616. The number satisfying the given condition is 2268072.

What are the Methods to Find LCM of 2601 and 2616?

The commonly used methods to find the LCM of 2601 and 2616 are:

Listing Multiples
Division Method
Prime Factorization Method

What is the Least Perfect Square Divisible by 2601 and 2616?

The least number divisible by 2601 and 2616 = LCM(2601, 2616)
LCM of 2601 and 2616 = 2 × 2 × 2 × 3 × 3 × 17 × 17 × 109 [Incomplete pair(s): 2, 109]
⇒ Least perfect square divisible by each 2601 and 2616 = LCM(2601, 2616) × 2 × 109 = 494439696 [Square root of 494439696 = √494439696 = ±22236]
Therefore, 494439696 is the required number.

If the LCM of 2616 and 2601 is 2268072, Find its GCF.

LCM(2616, 2601) × GCF(2616, 2601) = 2616 × 2601
Since the LCM of 2616 and 2601 = 2268072
⇒ 2268072 × GCF(2616, 2601) = 6804216
Therefore, the GCF = 6804216/2268072 = 3.

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