Question

Find 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

Answer 1

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

$a=bq+r$

Where $0\leq r$

$x=5q+1$

$x=12p+3$

$5q+1=12p+3$

$5q-12p=3-1$

$5q-12p=2$...(1)

When q=10 and p=4

Then,

$5(10)-12(4)=50-48=2$

q=10 and p=4 satisfied the equation (1)

Substitute q=10

$x=5(10)+1=51$

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.