Question

Find the smallest number which on dividing by 6 8 12 leaves the remainder 4 6 10 respectively

Answer 1

6×4=24

8×6=48

12×10=120

Answer 2

Let x be a smallest number which on dividing by 6,8 and 12 leaves the remainder 4,6 and 10 respectively.

To find:

Smallest number x

Solution:

$6=2\times 3$

$8=2\times 2^2$

$12=2\times 2\times 3$

LCM(6,8,12)=$2\times 3\times 4\times 6=144$

By using Euclid's division algorithm

$144=6\times 24+0$

$144=140+4=(6\times 23+2)+4$

$144-2=6\times 23+4$

$144=8\times 18+0$

$144=138+6=8\times 17+2+6$

$144-2=8\times 17+6$

$144=12\times 12+0$

$144=134+10$

$144=12\times 11+2+10$

$144-2=12\times 11+10$

$144-2=142$

Hence, 142 is the smallest number which on dividing by 6,8 and 12 leaves remainder 4,6 and 10 respectively.