Given:
Divisors: 12, 16, 24
Remainder = 4
Range = Between 4000 and 5000
Formula Used:
Required number = LCM of the divisors × k + Remainder
It should be less than or equal to 5000 and greater than or equal to 4000
Solution:
12 = 2² × 3
16 = 2⁴
24 = 2³ × 3
LCM = 2⁴ × 3 = 48
Let the required number be x, such that x ≡ 4 (mod 48) => x = 48k + 4
=> 48k + 4 ≤ 5000 => 48k ≤ 4996 => k ≤ 104
Take k = 104 => x = 48 × 104 + 4 = 4996
Therefore, the required highest number is 4996.
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