i am a number less than 3,000. when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44. what number i am i

Question

less than 3,000, when you divide by 32 the remainder is 30, when you divide by 58 the remainder is 44

Answer 1

find the LCM of 58 and 32

32=2x2x2x2x2

58=2x29

LCM=2x2x2x2x2x29=928

add 44 to 928 so that when 928 is divided by 58 there will be a remainder of 44 

928+44=972

when you divide the number you want by 32 and get a remainder of 30 the remainder will be 30/32=0.9375 as a decimal

972/32=30.375, wrong answer

subtract 58 from 972 to get 914

914/32=28.5625, wrong answer

note: every time you subtract 58, you get a number that, when divided by 58, leaves a remainder of 44

914-58=856 and 856/32=26.75, wrong answer

856-58=798

798 when divided by 58 leaves 44 (798/58=13 R44)

798/32=24.9375 which is what you want

798/32=24 R30

the number you are looking for is 798

note: there are others also

use the same reasoning

3*the LCM is 2784 is where to start...

doing the work...

2654 is another

2*the LCM=1856

doing the work...

1726 is another