find the greatest number of six digits which when divided by 20,24,36,40,48 leaves remainders 14,18,30,34,43
Answers
Given :- find the greatest number of six digits which when divided by 20,24,36,40,48 leaves remainders 14,18,30,34,42 ?
Solution :-
as we can see that,
- 20 - 24 = 6
- 24 - 18 = 6
- 36 - 30 = 6
- 40 - 34 = 6
- 48 - 42 = 6
since difference is same as 6 .
so,
→ smallest number which when divided by 20,24,36,40,48 leaves remainders 14,18,30,34,42 will be = LCM(20,24,36,40,48) - 6 .
prime factors of 20,24,36,40,48 are :-
→ 20 = 2 * 2 * 5
→ 24 = 2 * 2 * 2 * 3
→ 36 = 2 * 2 * 3 * 3
→ 40 = 2 * 2 * 2 * 5
→ 48 = 2 * 2 * 2 * 2 * 3
then,
→ LCM = 2 * 2 * 2 * 2 * 3 * 3 * 5 = 720
now,
→ Greatest 6 digit number is = 999999
then,
→ Multiple of 720 near 99999 is = 1388 * 720 = 999360 .
therefore,
→ Required number = 999360 - 6 = 999354 (Ans.)
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