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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