Question

The least number which when divided by 18, 12, 20 and 38 leaves remainders 16, 10, 18 and 36 respectively is

• A. 3400
• B. 3422
• C. 3420
• D. 3418

Answer 1

The correct option is D 3418

LCM of 18, 12, 20, 38:

18 = 2 × 3 × 3

12 = 2 × 2 × 3

20 = 2 × 2 × 5

38 = 2 × 19

∴ LCM $=2^2\times 3^2\times 5\times 19$

= 4 × 9 × 95

= 3420

∴ 3420 is the least number which is completely divisible by 18, 12, 20 and 38.

HCF of remainders 16, 10,18, 36:

16 = 2 × 2 × 2 × 2

10 = 2 × 5

18 = 2 × 3 × 3

36 = 2 × 2 × 3 × 3

∴ HCF = 2

Subtracting HCF from LCM, we get, 3420 – 2 = 3418.

Thus, the least number which when divided by 18, 12, 20 and 38 leaves remainders 16, 10, 18 and 36 respectively is 3418.

Hence, the correct answer is option (d).