The least common factor of 7 and 8, also known as the lowest common multiple or LCM, is 56. It is the smallest number that is divisible by both 7 and 8.
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Methods to Find the LCM of 7 and 8
There are three different methods to find the LCM of 7 and 8. They are:
- Listing Method
- Prime Factorization Method
- Division Method
LCM of 7 and 8 Using the Listing Method
The listing method is a simple approach to find the LCM. Here’s how you can find the LCM of 7 and 8 using this method:
- Write down the multiples of 7 and 8 separately.
- Identify the common multiples of 7 and 8.
- Choose the smallest common multiple as the LCM.
By applying this method, the LCM of 7 and 8 is found to be 56.
LCM of 7 and 8 Using the Prime Factorization Method
The prime factorization method is another way to find the LCM of 7 and 8. Follow these steps:
- Find the prime factors of 7 and 8.
- Write the prime factors in their exponent forms.
- Multiply the prime factors with the highest power.
- The result obtained is the LCM of 7 and 8.
Using this method, the LCM of 7 and 8 is calculated as 56.
LCM of 7 and 8 Using the Division Method
The division method is a systematic approach to find the LCM. Here’s how it works:
- Write the numbers, 7 and 8 in this case, for which you want to find the LCM.
- Find the smallest prime number that is divisible by either 7 or 8.
- Divide the numbers by the prime number and continue the process until you reach 1 in the entire row.
- Multiply all the prime numbers obtained to get the LCM.
By applying the division method, the LCM of 7 and 8 is found to be 56.
What Is the Formula for Finding the LCM of 7 and 8?
The LCM of 7 and 8 can be calculated using the formula: LCM(7, 8) = (7 8) / HCF(7, 8), where HCF represents the highest common factor or the greatest common divisor of 7 and 8. Another formula that can be used is: 7 8 = LCM(7, 8) * HCF(7, 8).
Problems Based on LCM of 7 and 8
Question 1: What is the least perfect square divisible by 7 and 8?
The least perfect square divisible by 7 and 8 can be found by calculating the LCM. By expanding the LCM of 7 and 8, we get 7 2 2 * 2. To make the pairs complete, we multiply 2 and 7 with it. Therefore, the least perfect square divisible by 7 and 8 is 784.
Question 4: If the LCM of two numbers is 56, HCF is 1, and one of the numbers is 8, find the other number.
Given that one number is 8, the LCM is 56, and the HCF is 1. Let the other number be x. Using the product of two numbers formula, we have 8 x = 56 1. Solving for x, we find that the other number is 7.
Frequently Asked Questions (FAQs)
Q: What is the LCM of 7 and 8?
A: The LCM of 7 and 8 is 56.
Q: Are LCM and HCF of 7 and 8 the same?
A: No, the LCM of 7 and 8 is 56, while the HCF is 1. Therefore, they are not the same.
Q: Are the LCM of 7 and 8 the same as the LCM of 4, 7, and 8?
A: Yes, the LCM of 7 and 8 is 56, which is also the LCM of 4, 7, and 8.
Q: Is 112 considered the LCM of 7 and 8?
A: No, 112 is a common multiple of 7 and 8, but it is not the lowest common number divisible by 7 and 8. The LCM is determined by focusing on the lowest common number, which in this case is 56.
We hope this article helps you understand the basics of finding the LCM of 7 and 8. If you’re looking to learn more about math, check out Wiingy’s Online Math Tutoring Services to learn from top mathematicians and experts.
