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. 148
B. 149
C. 150
D. 147
Answer: Option D
Solution(By Examveda Team)
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
This Question Belongs to Arithmetic Ability >> Problems On H.C.F And L.C.M
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