Finding the Least Common Multiple (LCM) of 3 and 5

Video what is the lcm of 3 and 5

What is the LCM of 3 and 5? The LCM of 3 and 5 is 15. The LCM, also known as the Least Common Multiple or Lowest Common Multiple, is the smallest number that is divisible by both 3 and 5.

Methods to Find the LCM of 3 and 5

There are three different methods for finding the LCM of 3 and 5. They are:

  1. Listing Method
  2. Division Method
  3. Prime Factorization Method

LCM of 3 and 5 Using the Listing Method

The listing method is one of the methods for finding the LCM. To find the LCM of 3 and 5 using the listing method, follow these steps:

  1. Write down the first few multiples of 3 and 5 separately.
  2. From the multiples of 3 and 5, focus on the ones that are common to both numbers.
  3. Take out the smallest common multiple, which will be the LCM of 3 and 5.

The LCM of 3 and 5 can be obtained using the listing method:

  • Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36…
  • Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45…

From the above multiples, it is clear that the least common multiple is 15. Therefore, the LCM of 3 and 5 is 15.

LCM of 3 and 5 Using the Division Method

The division method is another way to find the LCM. To find the LCM of 3 and 5 using the division method, follow these steps:

  1. Write down the numbers for which you want to find the LCM (3 and 5 in this case), separated by commas.
  2. Find the smallest prime number that is divisible by either 3 or 5.
  3. If any of the numbers between 3 and 5 is not divisible by the respective prime number, write that number in the next row and proceed further.
  4. Continue dividing the numbers obtained after each step by the prime numbers until you have 1 in the entire row.
  5. Multiply all the prime numbers, and the final result will be the LCM of 3 and 5.
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The LCM of 3 and 5 can be obtained using the division method:

  • Prime Factors:
  • First Number:
  • Second Number:

Therefore, the LCM of 3 and 5 is 3 * 5 = 15.

LCM of 3 and 5 Using the Prime Factorization Method

The prime factorization method is yet another approach to finding the LCM. To find the LCM of 3 and 5 using the prime factorization method, follow these steps:

  1. Find the prime factors of 3 and 5 using the repeated division method.
  2. Write all the prime factors in their exponent forms and multiply the prime factors with the highest power.
  3. The final result after multiplication will be the LCM of 3 and 5.

The LCM of 3 and 5 can be obtained using the prime factorization method:

  • Prime factorization of 3: 3 = 3^1
  • Prime factorization of 5: 5 = 5^1

Therefore, the LCM of 3 and 5 is 3^1 * 5^1 = 15.

What Is the Formula for Finding the LCM of 3 and 5?

The LCM of 3 and 5 can be calculated using the formula:

LCM(3, 5) = (3 * 5) / HCF(3, 5),

where HCF is the highest common factor or the greatest common divisor of 3 and 5.

Another formula for finding the LCM of 3 and 5 is:

3 5 = LCM(3, 5) HCF(3, 5),

which means that the product of 3 and 5 is equal to the product of their LCM and HCF.

Frequently Asked Questions (FAQs)

Q: Is 30 also considered as the LCM of 3 and 5?

A: No, 30 is not considered the LCM of 3 and 5. Although 30 is a common multiple of 3 and 5, it is not the lowest common number divisible by both 3 and 5. The LCM focuses on finding the lowest common number, which in this case is 15.

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Q: Are the LCM of 3 and 5 the same as the LCM of 1, 3, and 5?

A: Yes, the LCM of 3 and 5 is the same as the LCM of 1, 3, and 5, which is 15. Therefore, the LCM of 3 and 5 is the same as the LCM of 1, 3, and 5.

Q: What is the LCM of 3 and 5?

A: The LCM of 3 and 5 is 15.

Q: Are LCM and HCF of 3 and 5 the same?

A: No, the LCM of 3 and 5 is 15, while the HCF of 3 and 5 is 1. Therefore, the LCM and HCF of 3 and 5 are not the same.

We hope this article has helped you understand how to find the LCM of 3 and 5. If you want to learn more about math, consider exploring Wiingy’s Online Math Tutoring Services, where you can learn from top mathematicians and experts.

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