Question

The smallest 4-digits number, which is exactly divisible by 9,15,18, is

Answer 1

Answer:

The answer is 1080

Step-by-step explanation:

LCM of 9, 15, and 18 is 90

Smallest 4 digit number which divisible by 9,15,18 is 1080

Answer 2

Question

Find the smallest 4-digits number, which is exactly divisible by 9, 15 and 18.

$\rule{300}{1}$

Answer

Step 1: Find LCM of 9, 15 and 18.

Method 1: Prime Factorize 9, 15 and 18 separately.

$\begin{array}{r | l} 3 & 9 \\ \cline{2-2} 3& 3\\ \cline{2-2} &1 \\ \end{array}$

9 = 3×3

$\begin{array}{r | l} 3 & 15 \\ \cline{2-2} 5& 5\\ \cline{2-2} &1 \\\end{array}$

15 = 3×5

$\begin{array}{r | l} 2& 18 \\ \cline{2-2} 3& 9\\ \cline{2-2} 3& 3\\ \cline{2-2} & 1\\ \end{array}$

18 = 2×3×3

LCM of 9, 15 and 18 = 3×3×5×2 = 90

Method 2: Prime Factorize all numbers together.

$\begin{array}{r | l} 2 & 9,15,18\\ \cline{2-2} 3 & 9,15,9 \\ \cline{2-2} 3 &3,5,3 \\ \cline{2-2} 5& 1,5,1\\ \cline{2-2}&1,1,1 \\ \end{array}$

LCM of 9, 15 and 18 = 3×3×5×2 = 90

Step 2: Since 90 is a two digit number we will have to find a multiple of 90 which is closest to 1000.

90×10 = 900

90×11 = 990

90×12 = 1080

Step 3: Verify if 1080 is the accurate answer.

1080÷9 = 120

1080÷15 = 72

1080÷18 = 60

∴1080 is the smallest 4-digit number, which is exactly divisible by 9, 15 and 18.

$\rule{300}{1}$