Question:
Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
Solution:
First find the LCM of 20, 25, 35 and 40.
$\operatorname{LCM}(20,25,35,40)=2 \times 2 \times 2 \times 5 \times 5 \times 7=1400$
Now, we can see that
$20-14=6$
$25-19=6$
$35-29=6$
$40-34=6$
So, the required number would beLCM $(20,25,35,40)-6$
$=1400-6$
$=1394$
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