Question

Find the least 5 digit number which leaves reamainder 3 in each case when divide by 5'10'12'15,18,25, and30​

Answer 1

Answer:

10163

Step-by-step explanation:

first find lcm of divisors

seconed we have equation where remainder is 3 in all case

a=bq+3 where b are divisors leaving remainder 3

now ,we have least 5digit no 1000 now divide it by lcm

because to find no to be add or subtract to complete ly divide by lcm

here lcm is 240

so,here

number to be add or subtract to complete ly divide by 240

1000/240+r=factor of 240

r=160 now add it by 1000

=10160

now we have ,18160as least 5digit factor of all the numbers

now add 10160by 3 because in all case 3 is remainder

therefore,we have. 10163 as required answer