Question

1. Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
2. Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

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Answer 1

1.

Step 1: We need to find the LCM of the given numbers.

$\begin{array}{r | l} 2 & 4,10,9 \\ \cline{2-2} 2 & 2,5,9 \\ \cline{2-2} 5 & 1,5,9 \\ \cline{2-2} 3 & 1,1,9 \\\cline{2-2} 3 & 1,1,3 \\\cline{2-2} & 1,1,1 \\ \end{array}$

LCM of 4, 10, 9 is ⇒ $2\times2\times5\times3\times3 = 180$

Step 2: Now we need to pair the primes.

$(2\times2)\times5\times(3\times3 )= 180$

∴ 5 doesn't have a pair.

Step 3: So now we multiply 5 to 180.

$180\times 5 =900$

∴ 900 is the smallest square number that is divisible by each of the numbers 4, 9 and 10.

2.

Step 1: We need to find the LCM of the given numbers.

$\begin{array}{r | l} 2 & 8,15,20 \\ \cline{2-2} 2 & 4,15,10 \\ \cline{2-2} 5 & 2,15,5 \\ \cline{2-2} 2 & 2,3,1 \\\cline{2-2} 3 &1,3,1 \\\cline{2-2} & 1,1,1 \\ \end{array}$

LCM of 8, 15, 20 is ⇒ $2\times2\times5\times2\times3 = 120$

Step 2: Now we need to pair the primes.

$(2\times2)\times5\times2\times3 = 120$

∴ 5, 2 and 3 doesn't have a pair.

Step 3: So now we multiply $5\times2\times3$ to 120

$5\times2\times3\times120=3600$

∴ 3600 is the smallest square number that is divisible by each of the numbers 8, 15 and 20.