Question

find the least perfect square number divisible by each one of 24,32and56

Answer 1

Answer is in the pic above...

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Answer 2

$\: \: \: \: \: \: \: \: your \: \: \: \: answer \\ - - - - - - - - - - - - -$

$The \: \: least \: \: number \: \: divisible$

$by \: \: each \: \: one \: \: of \: \: 24 \: \: \: 32 \: \: \: 56$

$is \: \: their \: \: LCM$

$Now \: \: LCM \: \: of \: \: 24 \: \: \: 32 \: \: \: and \: \: 56$

$is \: \: (2 \times 2 \times 2 \times2 \times 3 \times2 \times 7) = 672$

$672 = 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 7 \\ \\ \: \: \: \: \: \: \: \: = 2 {}^{2} \times 2 {}^{2} \times 2 \times 3 \times 7 \\ \\ \: \: \: \: \: \: \: \:$

$To \: \: make \: \: it \: \: a \: \: perfect \: \: square \: \: \\ it \: \: must \: \: be \: \: multiplied \: \: by \\ (2 \times 3 \times 7) \: ,i.e. ,\: \: 42$

$Hence, \: \: required \: \: number \\ = 42 \times 672 \\ = 28224$