A Rope Can Be Cut Into An Equal Lenght With No Rope Left Over.The Lenght Can Be 15Cm, 18Cm Or 25Cm.What Is The Shortest Possible Lenght Of The Rope?

you want the LCM of 15, 18, and 25

multiply the prime factors ... 2 * 3 * 3 * 5 * 5

To find the shortest possible length of the rope that can be cut into equal lengths with no rope left over, we need to find the greatest common divisor (GCD) of the given lengths (15cm, 18cm, and 25cm). The GCD is the largest number that evenly divides all the given lengths.

To find the GCD, we can use the Euclidean algorithm:

Step 1: Find the GCD of the first two lengths, 15cm and 18cm.
- Divide 18 by 15: 18 ÷ 15 = 1 remainder 3
- Replace 18 with 15 and 15 with 3: 15 ÷ 3 = 5 remainder 0
- The GCD of 15cm and 18cm is 3.

Step 2: Find the GCD of 3 (previous result) and 25cm.
- Divide 25 by 3: 25 ÷ 3 = 8 remainder 1
- Replace 25 with 3 and 3 with 1: 3 ÷ 1 = 3 remainder 0
- The GCD of 3 and 25cm is 1.

Therefore, the shortest possible length of the rope is 1cm, which is the GCD of 15cm, 18cm, and 25cm.