Question

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

Options:
3400/3422/3420/3418

Answer 1

Step-by-step explanation:

Given that: The least number which when divided by 18 ,12,20 and 38 leaves remainder is 16 ,10, 18 and 36 respectively is___

Options:

3400/3422/3420/3418

Solution: To find that number

Step 1:Find the LCM of 18,12,20,38

$18 = 2 \times 3 \times 3 \\ 12 = 2 \times 2 \times 3 \\ 20 = 2 \times 2 \times 5 \\ 38 = 2 \times 19 \\ \\ LCM(18,12,20,38) = {2}^{2} \times {3}^{2} \times 5 \times 19 \\ \\ = 4\times 9 \times 5 \times 19 \\ \\ = 36 \times 5 \times 19 \\ \\ LCM(18,12,20,38) = 3420$

3420 is the least number which divided by 18,12,20 and 38 without leaving remainder.

Step 2: Take HCF of remainder 16,10,18,36

$16 = 2 \times 2 \times 2 \times 2 \\ 10 = 2 \times 5 \\ 18 = 2 \times 3 \times 3 \\ 36 = 2 \times 2 \times 3 \times 3 \\ \\ HCF(16,10,18,36) = 2$

Subtract HCF from LCM 3420-2= 3418

option 4 (3418) is that least number which when divided by 18 ,12,20 and 38 leaves remainder is 16 ,10, 18 and 36 respectively.

Hope it helps you.