Which smallest 4-digit number when divided by 12, 16, 18, and 20 leaves the remainder 21?

Question

Question

This question was previously asked in

Bihar STET TGT (Social Science) Official Paper-I (Held On: 08 Sept, 2023 Shift 5)

Answer 1

Concept Used:

Certainly, we can also solve the problem by finding the Least Common Multiple (LCM) of 12, 16, 18, and 20.

Calculation:

⇒ LCM(12,16,18,20) = 2⁴ × 3² × 5

⇒ LCM(12,16,18,20) = 720

Now, since the number should be at least 4 digit number If we multiply it by 2 we get (720 x 2) = 1440 (4-digit number),

But 1440 is divisible by 12, 16, 18, and 20. We must have 21 as the remainder.

So, we will add 21 in 1440.

⇒ 1440 + 21 = 1461

∴ The correct answer is "1461".