Question

find the least number of five digits that is exactly divisible by 9,12,15,18 and 24​

Answer 1

$\bf\large{\underline{Question:-}}$

find the least number of five digits that is exactly divisible by 9,12,15,18 and 24.

$\bf\large{\underline{Solution:-}}$

★ NOTE, The greatest 5 digit number is 99999

★ Now,

finding the L.C.M of 9,12,15,18,24

2 | 9 , 12 , 15, 18 , 24

2 | 9 , 6 , 15 , 9 , 12

2 | 9 , 3 , 15 , 9 , 6

3 | 9 , 3 , 15 , 9 , 3

3 | 3 , 1 , 5 , 3 , 1

5 | 1 , 1, ,5 , 1, 1

| 1 , 1 , 1 , 1 , 1

L.C.M of {9,12,15,18 and 24} = 2×2×2×3×3×5

L.C.M of {9,12,15,18 and 24} = 360

Then,

Divide it by 99999 by 360

we get remainder = 279

Now,

subtract the remainder from 99999

→ 99999 - 279

→ 99720

threfore,

the required number which is exactly divisible by 9,12,15,18,24 is 99720.