Measuring rods problem — find the shortest cloth length measured exactly by each Three measuring rods are 64 cm, 80 cm, and 96 cm long. What is the least length of cloth that can be measured an exact number of times using any one of these rods (i.e., the least common multiple in meters)?

Introduction / Context:
This is a classic least common multiple (LCM) application. The “least length of cloth measured exactly by each rod” means we need a length that is simultaneously a multiple of 64 cm, 80 cm, and 96 cm, and as small as possible. Converting to meters at the end makes the answer presentation consistent with the options.

Given Data / Assumptions:

• Rod lengths: 64 cm, 80 cm, 96 cm.
• We want the least positive length that is a multiple of all three.
• Final answer must be shown in meters.

Concept / Approach:
The LCM of integers a, b, c can be found by prime factorization or successive LCM calculations. LCM captures the smallest number divisible by all inputs.

Step-by-Step Solution:
64 = 2^6.80 = 2^4 * 5.96 = 2^5 * 3.Take the highest power of each prime across all: for 2 → 2^6; for 3 → 3^1; for 5 → 5^1.LCM = 2^6 * 3 * 5 = 64 * 15 = 960 cm.Convert to meters: 960 cm = 9.60 m.

Verification / Alternative check:
9.60 m = 960 cm. Now 960 ÷ 64 = 15, 960 ÷ 80 = 12, 960 ÷ 96 = 10, all integers, so 960 cm works. Any smaller number would miss at least one divisibility requirement.

Why Other Options Are Wrong:
0.96 m is only 96 cm, not divisible by 80. 19.20 m and 96.00 m are multiples of 9.60 m but not the least. 6.40 m (640 cm) fails divisibility by 96.

Common Pitfalls:
Taking the greatest common divisor (GCD) by mistake, or converting to meters too early and introducing rounding errors. Always compute LCM in centimeters first.

Final Answer:
9.60 m