Find the least number which when divided by 20, 25, 30 and 36 leaves a remainder 4 in each case.

Given :

The given statement is the least number which when divided by 20, 25, 30, and 36 leaves a remainder of 4 in each case.

To do :

We have to find the least number.

Solution :

The least number is the L.C.M. $(20, 25, 30, 35) + 4$.

L.C.M. of 20, 25, 30 and 35 

$20 = 2 \times 2 \times 5$

$25 = 5 \times 5$

$30 = 2 \times 3 \times 5$

$36 = 2 \times 2 \times 3 \times 3$

L.C.M. of 20, 25, 30 and 36 $= 2 \times 2 \times 3 \times 3 \times 5 \times 5  = 900$

Now, 

$900 + 4 = 904$

Hence, 904 is the least number which when divided by 20, 25, 30, and 36 leaves a remainder of 4 in each case.