Question

Find the greatest 3- digit number that is
exactly divisible by 6, 15 and 21

Answer 1

Answer:

210 is the greatest 3 digit number which can be divided by 6,15 and 12

Answer 2

$i)Let's \:find \: smallest \: number \: divisible \\by \: 6, 15 \:and \: 21$

$\red{ Smallest \: number \:divisible \: by }\\\red{ \:6, 15 \:and \: 21} \\= LCM \: of \: 6, 15 \:and \:21$

Finding L.C.M:

3| 6, 15 , 21

___________

*** 2 , 5 , 7

$L.C.M \: of \: 6, 15 \: and \: 21\\ = 3 \times 2 \times 5 \times 7 \\= 210$

$ii ) Now, we \:need \: to \: find \: greatest \\3-digit \:number \: divisible \:by \: 6,15 \:and \:21$

$We \: know \:that,\\ Greatest \: 3 \: digit \:number \: 999$

Dividing 999 by 210:

210 | 999 | 4

****** 840

_________

********159

$Remainder = 159$

$\red{ Required \: number } \\= 999 - Remainder \\= 999 - 159 \\= 840$

Therefore.,

$\green { 840 \: is \:the \: greatest \: 3 \:digit \: number }$

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