Answer:
59
Step-by-step explanation:
If a number is divided by [tex]n[/tex] and leaves a remainder [tex](n-1)[/tex], then the number [tex](n+1)[/tex] will be completely divisible by [tex]n[/tex].
Therefore, when we say a number [tex]x[/tex], when divided by 6, it leaves a remainder 5, then ([tex]x+1[/tex]) will be a multiple of 6.
When we say a number [tex]x[/tex], when divided by 5, it leaves a remainder 4, then ([tex]x+1[/tex]) will be a multiple of 5.
When we say a number [tex]x[/tex], when divided by 4, it leaves a remainder 3, then ([tex]x+1[/tex]) will be a multiple of 4.
When we say a number [tex]x[/tex], when divided by 3, it leaves a remainder 2, then ([tex]x+1[/tex]) will be a multiple of 3.
So, [tex]x+1[/tex] is a common multiple of 3, 4, 5 and 6.
Taking LCM of 3, 4, 5 and 6, we get 60.
So, the number 60 - 1 = 59 is the least such number.
