find the least number of five digits that is exactly divisible by 9,12,15,18 and 24
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find the least number of five digits that is exactly divisible by 9,12,15,18 and 24
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[tex]\bf\large{\underline{Question:-}}[/tex]
find the least number of five digits that is exactly divisible by 9,12,15,18 and 24.
[tex]\bf\large{\underline{Solution:-}}[/tex]
★ 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.