Question

Number when divided by 2 3 7 leaves a remainder 2 3 4 . Findr emainder when divided by 105

Answer 1

Answer:

Step-by-step explanation:

Let x be the number,

x = 5 * a + 2

x = 3 * b + 2

x = 7 * c + 2

Where a, b and c are integers

For x to satisfy all the three equations x has to the LCM of 3, 5 and 7.

LCM ( 3, 5, 7 ) = 3 * 5 * 7 (as 3, 5 and 7 are co prime numbers and hence their LCM is a product of the 3 numbers)

So x =( 3 * 5 * 7) * a + 2

x = 105 * a + 2

Hence plug in the non negative integral values of a and get the series of number.

The smallest number is obtained when a = 1

Hence the first number is

x = 105 + 2

x = 107