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.
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Methods to Find the LCM of 3 and 5
There are three different methods for finding the LCM of 3 and 5. They are:
- Listing Method
- Division Method
- 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:
- Write down the first few multiples of 3 and 5 separately.
- From the multiples of 3 and 5, focus on the ones that are common to both numbers.
- 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:
- Write down the numbers for which you want to find the LCM (3 and 5 in this case), separated by commas.
- Find the smallest prime number that is divisible by either 3 or 5.
- 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.
- Continue dividing the numbers obtained after each step by the prime numbers until you have 1 in the entire row.
- Multiply all the prime numbers, and the final result will be the LCM of 3 and 5.
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:
- Find the prime factors of 3 and 5 using the repeated division method.
- Write all the prime factors in their exponent forms and multiply the prime factors with the highest power.
- 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.
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.
