Question

What is the least multiple of 19, which when divided by 6, 8, 10 and 12 Ieaves remainder 1. 3, 5 and 7 respectively? (b) 550 (a) 375 (c) 400 (d) 475​

Answer 1

Answer:

sorry bro don't know.........

Answer 2

Answer:

option (d) 475

Step-by-step explanation:

Here in each case, the difference between divisor and remainder is same, 5

6 – 1 = 5

8 – 3 = 5

10 – 5 = 5

12 – 7 = 5

Now, the number is divided by 6, 8, 10 and 12

∴ The LCM of 6, 8, 10, 12 = 120

Now it is given that the required number should be a multiplier of 13

∴ The required number should be (120x – 5); where ‘x’ is a variable

Now, we can write (120x – 5) as (114x + 6x – 5); where 114x is exactly divisible by 19

∴ To make the number (120x – 5) exactly divisible by 19, (6x – 5) must be divisible by 19

Now, if x = 4, then (6x – 5) = 19, which is exactly divisible by 19

∴ Our required number is (120 × 4 – 5) = 475