(4. Determine the greatest 5-digit number which is
exactly divisible by each of 8, 15 and 21. step by step solution
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(4. Determine the greatest 5-digit number which is
exactly divisible by each of 8, 15 and 21. step by step solution
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Answer:
99960
Step-by-step explanation:
By investigating the prime factorizations of 8 (2x2x2), 15 (3x5), and 21 (3x7), you can determine that their Least Common Multiple is 2x2x2x3x5x7 which is 840. The greatest 5 digit number is 99999. When you divide that by 840, you get 119 and a remainder. So your answer is 840x119 = 99960.
Verified answer
Tᴏ Fɪɴᴅ :- The Greatest 5 digit number exactly divisible by 8 , 15, and 21 ?
Sᴏʟᴜᴛɪᴏɴ :-
The greatest 5-digit number is 99999.
Now, Find the LCM of 8 , 15, and 21.
3 | 8 15 21
2 | 8 5 7
2 | 4 5 7
2 | 2 5 7
5 | 1 5 7
7 | 1 1 7
| 1 1 1
LCM :- 3 * 2 * 2 * 2 * 5 * 7 = 840.
Now, Divide 99999 by 840 so that we get the remainder...
→ 99999 = 840 * 119 + 39
Remainder we get is 39.
Now, Subtract the remainder from 99999.
→ 99999 - 39 = 99960 (Ans.)
Hence, The required number is 99960 which is exactly divisible by by 8 , 15 and 21.