Given:
When x is divided by 12, 15, 18, 20, 25
Remainder = 5
x is divisible by 7
Formula Used:
If x leaves remainder r when divided by several numbers: x − r is divisible by their LCM.
General form: x = LCM × k + r
Solution:
LCM(12,15,18,20,25):
12 = 2² × 3
15 = 3 × 5
18 = 2 × 3²
20 = 2² × 5
25 = 5²
=> LCM = 2² × 3² × 5² = 900
So, x − 5 = 900k
=> x = 900k + 5
x divisible by 7
=> 900k + 5 ≡ 0 (mod 7)
Least k = 4 => x = 900 × 4 + 5 = 3605
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