When 8, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 3, but x is divisible by 7. What is the value of x?

Correct option is A

Given :

When 8, 16, 18, 20 and 25 divide the least number (x), the remainder in each case is 3. Also, (x) is divisible by 7.

Concept Used :
If a number x leaves the same remainder r when divided by several numbers, then
x - r = LCM of the given divisors

Solution :

Since the remainder in each case is 3,
x - 3 is divisible by 8, 16, 18, 20 and 25

Now find LCM of (8, 16, 18, 20, 25):

​$$\text{LCM} = 2^4 \times 3^2 \times 5^2 = 3600$$​​

So,
x - 3 = 3600
x = 3603

Now check divisibility by 7:
3$$603 \div 7 = 514.71 \ (\text{not divisible})$$​​

Next number:
x - 3 = 3600 + 3600 = 7200
x = 7203

Check divisibility:
7203 $$\div$$​ 7 = 1029  (divisible)
Answer : 7203