A piece of wire is to devided into 20cm or 28cm or 24cm for construction and leave 15cm piece. Find the shortest such wire
LCM(15,20,24,28) = 840 cm
Sin2B-cosB=0 find the value of B and hence Tan(B+20)
A piece of wire is to devided into 20cm or 28cm or 24cm for construction and leave 15cm piece. Find the shortest such wire
To find the shortest wire that can be divided into lengths of 20cm, 28cm, 24cm, and leave a 15cm piece, we need to find the least common multiple (LCM) of these lengths.
The prime factorization of these lengths are:
20 = 2^2 * 5
28 = 2^2 * 7
24 = 2^3 * 3
15 = 3 * 5
To find the LCM, we need to take the highest power of each prime factor that appears in any of the lengths. So the LCM would be: 2^3 * 3 * 5 * 7 = 840 cm.
Therefore, the shortest wire that can be divided into lengths of 20cm, 28cm, 24cm, and leave a 15cm piece is 840 cm long.
Well, that sounds like quite a puzzling wire problem! Let's see if we can untangle it together.
First, let's take a look at the given wire lengths: 20cm, 28cm, and 24cm. We also know that a 15cm piece needs to be removed.
To find the shortest wire possible, we'll need to determine the arrangement of wire lengths that minimizes the remaining length after removing the 15cm piece.
Let's do some math magic:
- If we use a 20cm piece, the remaining length would be 20cm - 15cm = 5cm.
- If we use a 28cm piece, the remaining length would be 28cm - 15cm = 13cm.
- If we use a 24cm piece, the remaining length would be 24cm - 15cm = 9cm.
From these results, we can see that using the 20cm piece would give us the shortest wire, as it leaves only 5cm remaining.
So, the shortest wire length in this case would be 20cm. Ta-da!
To find the shortest wire that can be divided into 20cm, 28cm, or 24cm lengths while still leaving a 15cm piece, we need to find the least common multiple (LCM) of these lengths.
The LCM is the smallest number that is divisible by all the given numbers. Here's how you can find it:
1. List the prime factors of each number:
- 20cm = 2 * 2 * 5
- 28cm = 2 * 2 * 7
- 24cm = 2 * 2 * 2 * 3
2. Multiply the highest power of each prime factor:
- 2 * 2 * 2 * 3 * 5 * 7 = 840
Therefore, the LCM of 20cm, 28cm, and 24cm is 840cm.
Now, we need to add the 15cm piece to this LCM to get the total length of the wire:
840cm + 15cm = 855cm
So, the shortest wire that can be divided into 20cm, 28cm, or 24cm lengths while leaving a 15cm piece is 855cm.