Question:

Three measuring rods are of lengths \(120 \, \text{cm}, 100 \, \text{cm}\) and \(150 \, \text{cm}\). Find the least length of a fence that can be measured an exact number of times using any of the rods. How many times each rod will be used to measure the length of the fence?

Show Hint

For such problems, always use LCM to find the least common length and then divide to find number of uses.
Updated On: May 20, 2025
Hide Solution
collegedunia
Verified By Collegedunia

Solution and Explanation

Find LCM of \(120, 100, 150\) Prime factorisations: \[ 120 = 2^3 \times 3 \times 5 \] \[ 100 = 2^2 \times 5^2 \] \[ 150 = 2 \times 3 \times 5^2 \] LCM: \[ = 2^3 \times 3 \times 5^2 = 600 \, \text{cm} \] Number of times: \[ \frac{600}{120} = 5, \; \frac{600}{100} = 6, \; \frac{600}{150} = 4 \]
Was this answer helpful?
0
0

Questions Asked in CBSE X exam

View More Questions