Find a least number which when divided by 12 15 18 and 20 leaves a reminder 5 in each case.
Answers
Answered by
28
Solution :-
Here, we have to find a least number so that which when divided by 12 , 15 , 18 and 20 leaves a remainder 5
Therefore,
LCM of 12 , 15 , 18 and 20
12 = 2 * 5 * 2.
15 = 3 * 5
18 = 3 * 3 * 2
20 = 2 * 2 * 5
LCM = 2 * 2 * 3 * 3 * 5 = 180
Therefore,
The least number is 180 + 5 = 185
Verification :-
1) 185/ 12
Here, Quotient = 15
Remainder = 5
2) 185/15
Quotient = 12
Remainder = 5
3) 185/18
Quotient = 10
Remainder = 5
4) 185/20
Quotient = 9
Remainder = 5
Hence, The least number is 185.
Answered by
8
Question :-
- Find a least number which when divided by 12 15 18 and 20 leaves a reminder 5 in each case.
Answer :-
- The least number is 185.
Solution :-
- Here, we have to find a least number so that which when divided by 12 , 15 , 18 and 20 leaves a remainder 5
- so, we have to take the LCM
- LCM of 12 , 15 , 18 and 20
- 12 = 2 * 5 * 2.
- 15 = 3 * 5
- 18 = 3 * 3 * 2
- 20 = 2 * 2 * 5
- LCM = 2 * 2 * 3 * 3 * 5 = 180
Therefore,
- The least number is 180 + 5 = 185
⚽ Verification ⚽
1) 185/ 12
- Quotient = 15
- Remainder = 5
2) 185/15
- Quotient = 12
- Remainder = 5
⚽Verified⚽
Hence,
- The least number is 185.
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