Question

Find the smallest square number that
is divisible by each of the numbers 8,
15 & 20 ​

Answer 1

$\large \bold{ \underline{ \underline{ \: Answer : \: \: \: }}}$

$\to$ The required square number is 3600

$\large \bold{ \underline{ \underline{ \: Explaination : \: \: \: }}}$

Prime factorisation of 8 , 15 and 20 are :

$\to$ 8 = 2 × 2 × 2

$\to$ 15= 3 × 5

$\to$ 20 = 2 × 2 × 5

LCM of 8 ,15 and 20 is 2 × 2 × 2 × 3 × 5 i.e 120

Here , prime factors 2 , 3 and 5 do not have their respective pairs

Therefore , 120 is not a perfect square

Therefore , 120 should be multiplied by 2 × 3 × 5 i.e 30 to obtain a perfect square

Hence , the required square number is 120 × 2 × 3 × 5 = 3600