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A number x is divided by 7. When this number is divided by 8, 12 and 16. It leaves a remainder 3 in each case. The least value of x is = ?

A number x is divided by 7. When this number is divided by 8, 12 and 16. It leaves a remainder 3 in each case. The least value of x is = ? Correct Answer 147

LCM of 8, 12 and 16 = 48
∴ Required number = 48a + 3
Which is divisible by 7
∴ x = 48a + 3
      = 7 × 6a + 6a + 3
      = (7 × 6a) + (6a + 3) which is divisible by 7
i.e., 6a + 3 is divisible by 7
When a = 3, 6a + 3 = 18 + 3 = 21 which is divisible by 7
∴ x = 48 × 3 + 3
      = 144 + 3
      = 147

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