Find the least number of 5 digit that is exactly divisible by 16,18,24 and 30

Solution:

To find  the least number which exactly divisible by 16 , 18 , 24 , 30  we have to LCM

LCM of  16 , 18 , 24 , 30

Multiples of 16  -   16 , 32 , 48 , 64 , 80 ..........720.....

Multiples of 18  -  18 , 36 , 54 , ..........720....

Multiples of 24  - 24 , 48 , 72 .......720.....

Multiples of 30  - 30 , 60 , 90 .........720....

LCM  of   16 , 18 , 24 , 30  is  720

but 720  is the 3 digit number.  We have to find the least 5 digit number that is divisible by    16 , 18 , 24 , 30

Least  digit number is 10000

divide 10000 by 720 

$\frac{10000}{720}$  =  13.8

Next whole number is 14

So multiply 720 by 14

720 $\times$ 14  =  10080.

So, 10080 is the least 5 digit number that is divisible by    16 , 18 , 24 , 30