Question

what is lcm for 1,2,3,4,5,6,7,8,9,10 and show how you get the answer

Answer 1

We can try to do some prime factorization. The highest prime in this list is 7, so we look at each number in terms of its prime factors:

\begin{align}
1 &= 2^0 \times 3^0 \times 5^0 \times 7^0\\
2 &= 2^1 \times 3^0 \times 5^0 \times 7^0\\
3 &= 2^0 \times 3^1 \times 5^0 \times 7^0\\
4 &= 2^2 \times 3^0 \times 5^0 \times 7^0\\
5 &= 2^0 \times 3^0 \times 5^1 \times 7^0\\
6 &= 2^1 \times 3^1 \times 5^0 \times 7^0\\
7 &= 2^0 \times 3^0 \times 5^0 \times 7^0\\
8 &= 2^3 \times 3^0 \times 5^0 \times 7^0\\
9 &= 2^0 \times 3^2 \times 5^0 \times 7^0\\
10 &= 2^1 \times 3^0 \times 5^1 \times 7^0
\end{align}

Answer 2

Yeah, I started with 7 too. 840 is divisible by everything except 9

Answer 3

To find the LCM, you can then multiply the highest power of each prime. In this case, we have \(2^3\), \(3^2\), \(5^1\), and \(7^1\):

\[2^3 \times 3^2 \times 5^1 \times 7^1 = 6 \times 9 \times 5 \times 7 = 1890\]

If I'm not mistaken.

Answer 4

Nice

Answer 5

Hah. Whoops. In my original list, I forgot to list \(7^1\) as the correct value for 7. Fortunately, I didn't make that mistake when I multiplied things out :)

Answer 6

the answer is 2520 but i dont know how to get it

Answer 7

Yeah, 1890 isn't divisible by 8

Answer 8

I like your method shadow. I hope you can find your mistake

Answer 9

Lol. Blah O_O

Answer 10

2^ 3 ×3^ 2 ×5 ×7 =8×9×5×7=2520

Answer 11

2^3=8

Answer 12

Wait, you mean 2^3 isn't 6? Lol.

Thanks. Epic failure on my part.

Answer 13

:D

Answer 14

So it does work. I love it

Answer 15

Shadow deserves the medal for this one. He made a simple mistake, but provided the technique. Marina also deserves one for correcting the mistake

Answer 16

I agree. shadow did most of the work and explanation.