Question

Find the least number which on adding 9 to it becomes exactly divisible by 15 20 30 and 45

Answer 1

Answer:

The number which is divisible by 15 , 25 , 30, 45 is 450 (lcm of these numbers is 450). The least number which on addition of 9 is divisible by above numbers is 441.

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Answer 2

Given

On adding 9 to a number it becomes divisible by 15, 20, 30 and 45.

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To Find

The least number that we could add 9 to to make it divisible by 15, 20, 30 and 45.

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Solution

Step 1: Find the LCM of 15, 20, 30 and 45.

$\begin{array}{r | l} 2 & 15,20,30,45 \\ \cline{2-2} 2 & 15,10,15,45 \\ \cline{2-2} 3 & 15,5,15,45 \\ \cline{2-2} 3& 5,5,5,15 \\ \cline{2-2}5 & 5,5,5,5\\ \cline{2-2} & 1,1,1,1\\ \end{array}$

LCM of 15, 20, 30 and 45 is ⇒ 2×2×3×3×5 = 180

Step 2: Subtract 9 from the product.

180 - 9 = 171

∴ 171 is the least number which on adding 9 it becomes exactly divisible by 15, 20, 30 and 45.

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