Question

9. Find the greatest number of 4 digits which on being divided by 75, 90, 120 leaves the remainder 9 in each case.​

Answer 1

Ans : 9009

Step-by-step explanation:

$gretest \: number \: of \: 4 \: digit \: is9999$

$lcm \: of \: 75 \: 90 \: and \: 120$

LCM of 75 , 90 , 120 = 1800

$1800)9999(5 \\ \: \: \: \: \: \: \: \frac{ - 9000 \: \: \: \: }{999}$

$hence \: the \: number = \\ = (9999 - 999) + 9 \\ = 9000 + 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 9009 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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