The largest number of four digits which, when divided by 6, 12 and 18 leaves the same remainder 5 in each case is:
Given:
The number leaves a remainder of 5 when divided by 6, 12, and 18.
Formula Used:
N = LCM(6, 12, 18) × k + 5
Solution:
LCM(6, 12, 18) = 36
N = 36k + 5
Largest possible value of N is 9999.
36k + 5 ≤ 9999
36k ≤ 9994
k ≤ ≈ 277.61
N = 36 × 277 + 5 = 9972 + 5 = 9977
Thus, the largest number of four digits which, when divided by 6, 12, and 18, leaves the same remainder of 5 is 9977.
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