The greatest number for four digits which when divided by 12,16,and 24 leave remainder 2,6 and 14 respectively is = ?

Explanation:-

12 - 2 = 10
16 - 6 = 10
24 - 14 = 10
LCM of (12, 16, 24) = 6 × 2 × 4 × 1 = 48
Greatest number of four digits = 9999
∴ When it is divided by 48 we get remainder = 15
⇒ The greatest number of 4 digits which completely divides the given number is = 9999 - 15 = 9984
∴ number is = 9984 - 10 = 9974