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Question

The smallest positive integer n' with 24 divisors (where 1 and n are also considered as divisors of n) is

A
420
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B
240
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C
360
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D
480
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Solution

The correct option is C 360
Letusinvestigatetheoptionsaspertheguidelinesofthegivenpassage.OptionA420=22×31×231a=2,b=1,c=1numberofdivisors=(2+1)(1+1)(1+1)=1224.OptionB240=24×31×51a=4,b=1,c=1numberofdivisors=(4+1)(1+1)(1+1)=2024.OptionC360=23×32×51a=3,b=2,c=1numberofdivisors=(3+1)(2+1)(1+1)=24.OptionD480=25×31×51a=5,b=1,c=1numberofdivisors=(5+1)(1+1)(1+1)=24.BothoptionCandDcomplieswiththegivenguidence.ButoptionCi.e360islesser.AnswerOptionC

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