A number p is divisible by 7. When this number is divided

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

1. 148
2. 149
3. 150
4. 147

Correct Option: D

We get LCM of 8, 12 and 16 = 48
∴ Required number = 48a + 3 which is divisible by 7.
∴ p = 48a + 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.
∴ p = 48 × 3 + 3 = 144 + 3 = 147
Hence , The least value of p is 147 .