Question

Arnold had three pieces of different color string all the same length. Arnold cut the blue
string into 3 equal lengths. He cut the red string into 5 equal-size lengths, and the green
string into 15 equal-size lengths. He needs to cut the string so each color has the same
number of equal-size lengths.
What is the least number of equal-sized lengths each color string could have?
The least number of equal-sized lengths each color string could have is

Answer 1

Given ↷

No. of strings Arnold had ⇢3

• RED↝5 equal size
• GREEN↝15 equal size
• BLUE↝3 equal size

To find↷

least number of equal-sized lengths each color string could have

Solution↷

To find the least number of equal-sized lengths of each color, we'll find the least common factor of 3,5&15

• Least common factor or LCM⇢The smallest number, other than zero, that is a multiple of two or more given numbers

prime factor of 3 ⇢1 x 3

prime factor of 5⇢ 1 x 5

prime factor of 15⇢ 1 x 3 x 5

so,

LCM of 3,5,15 ⇢ 1 x 3 x 5 = 15

Hence, 15 is the least number of equal size lengths each color string could have.