Question

"Three monkeys climb 18m,45m and 72m respectively. Find the length of the longest tape that can measure these distances exactly"

Answer 1

Least Common Multiple

Given: three monkeys climb 18 m, 45 m and 72 m

To find: the length of the longest tape that can measure these distances exactly

Solution:

• We must understand that in order to find the length of the longest tape, we have to find the lcm of 18, 45 and 72.

• We prime factorise the numbers.

• Now, 18 = 2 × 3 × 3
• 45 = 3 × 3 × 5
• 72 = 2 × 2 × 2 × 3 × 3
• Thus, lcm (18, 45, 72) = 2 × 2 × 2 × 3 × 3 × 5
• = 360

Answer: the length of the longest tape that can measure these distances exactly is 360 m.

Answer 2

Step-by-step explanation:

$3 \times 3 \times 2 \times 2 \times 2 \times 5$