Answer:
51
Step-by-step explanation:
Let x be the number
When x divided by 5 then it gives remainder 1 and when divided by 12 gives remainder 3.
We have to the value of x.
Using Euclid's algorithm
[tex]a=bq+r[/tex]
Where [tex]0\leq r<b[/tex]
[tex]x=5q+1[/tex]
[tex]x=12p+3[/tex]
[tex]5q+1=12p+3[/tex]
[tex]5q-12p=3-1[/tex]
[tex]5q-12p=2[/tex]...(1)
When q=10 and p=4
Then,
[tex]5(10)-12(4)=50-48=2[/tex]
q=10 and p=4 satisfied the equation (1)
Substitute q=10
[tex]x=5(10)+1=51[/tex]
Hence,51 is the least counting number which when divided by 5 gives the remainder of 1 and when divided by 12 gives us the remainder of 3.
