Question

Find the least number of five digits which is exactly divisible by each of 8,12,18,40,and 45​

Answer 1

10080

why because 8=2

3

12=3×4=2

2

×3

18=9×2=2×3

2

40=10×4=2

3

×5

45=5×9=3

2

×5

So, to find LCM we have to take highest power among all number of each occurring factor, and multiply them to find LCM

here, prime factors appearing are 2,3,5

So, highest factor of 2 is 3, of 3 is 2 and of 5 is 1.

∴LCM=2

3

×3

2

×5=360

So, let to find the least number of 5 digits divisible by given numbers is x

⇒x>9999

360

x

>

360

9999

=

36

999.9

=27.775

x is completely divisible by 360 So,

360

x

is an integer.

So, we need to find next integer greater than 27.775

So, completely divisible 5 digit number by 360 is 360×28=10080

The least number of five digits which is exactly divisible by each of 8,12,18,40 and 45 is 10080

Answer 2

answer is 465857858787595