What is the least common multiple of 8 and 10
The prime factorization of 8 is $2^3$, and the prime factorization of 10 is $2\cdot 5$. The LCM must include all the prime factors of both numbers, raised to the highest powers they appear in either factor. Therefore, the LCM is $2^3\cdot 5=\boxed{40}$.
What is the least common multiple of 8 and 10...
The prime factorization of 8 is $2^3$, and the prime factorization of 10 is $2\cdot 5$. The LCM must include all the prime factors of both numbers, raised to the highest powers they appear in either factor. Therefore, the LCM is $2^3\cdot 5=\boxed{40}$.
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I apologize as I am not sure what I need to fix. Could you please clarify the issue?
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I apologize but I still do not understand what I need to fix. Can you please provide me with more information or context so I can better assist you?
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8 and 10
8 = 2*2*2
10= 2*5
the LCM is 2*2*2*5 = 40
(I think somewhere is that gibberish the bot did have 40)
I am sorry about that earlier confusion. Yes, you are correct. The prime factorization of 8 is $2^3$, and the prime factorization of 10 is $2\cdot 5$. The LCM must include all the prime factors of both numbers, raised to the highest powers they appear in either factor. Therefore, the LCM is $2^3\cdot 5=\boxed{40}$. Thank you for correcting me.
To find the least common multiple (LCM) of two numbers, you need to find the smallest number that is divisible by both of them. Here's how you can calculate the LCM of 8 and 10:
Step 1: Find the prime factorization of each number:
- Prime factorization of 8: 2 * 2 * 2 = 2^3
- Prime factorization of 10: 2 * 5
Step 2: Identify the highest exponent for each prime factor:
- Highest exponent of 2: 3
- Highest exponent of 5: 1
Step 3: Multiply the prime factors with their highest exponents to find the LCM:
- LCM = 2^3 * 5 = 8 * 5 = 40
Therefore, the least common multiple (LCM) of 8 and 10 is 40.