Find the least number of 7 digits that is exactly divisible by 16,18,24 and 30.
Answers
AnsWer :
1,000,080.
SolutioN :
Condition : The least number of 7 digits be 1000000.
Let the number be
- N1 = 16.
- N2 = 18.
- N3 = 24.
- N4 = 30.
Now,
2 | 16
2 | 8
2 | 4
2 | 2
| 1
_______________
2 | 18
3 | 9
3 | 3
| 1
_______________
2 | 24
2 | 12
2 | 6
3 | 3
| 1
_______________
3 | 30
2 | 10
5 | 5
| 1
LCM → 16 , 18 , 24 and 30
→ 2 * 2 * 2 * 2 , 2 * 3 * 3 , 2 * 2 * 2 * 3 , 3 * 2 * 5
→ 2⁴ * 3² * 5.
→ 720.
_______________
Now, Let
- Dividend = The least number of 7 digits.
- Divisior = 720.
720 ) 1000000 ( 1388
720
_________
2800
2166
__________
6400
5760
___________
6400
5760
__________
640
- So, We can write as, The least number of 7 digits = 1000000.
- Required number is 1000000 + ( Divisior - Remainder )
→ 1,000,000 + ( 720 - 640 )
→ 1,000,000 + ( 80 )
→ 1,000,080.
________________________________
VerificatioN :
- N1 = 16.
Let check N1 is exactly divisible by 1,000,080
→ 1,000,080 / N1
→ 1,000,080 / 16
→ 62,505.
__________________
- N2 = 18.
→ 1,000,080 / N2
→ → 1,000,080 / 18
→ 55,560.
__________________
- N3 = 24.
→ 1,000,080 / N3
→ → 1,000,080 / 24
→ 41,670.
__________________
- N4 = 30.
→ 1,000,080 / N4
→ → 1,000,080 / 30
→ 33,336.
Therefore, the value of 7 least digits number that is exactly divisible by 16,18,24 and 30 is 1,000,080.
Answer:
AnsWer :
1,000,080.
SolutioN :
Condition : The least number of 7 digits be 1000000.
Let the number be
N1 = 16.
N2 = 18.
N3 = 24.
N4 = 30.
Now,
2 | 16
2 | 8
2 | 4
2 | 2
| 1
_______________
2 | 18
3 | 9
3 | 3
| 1
_______________
2 | 24
2 | 12
2 | 6
3 | 3
| 1
_______________
3 | 30
2 | 10
5 | 5
| 1
LCM → 16 , 18 , 24 and 30
→ 2 * 2 * 2 * 2 , 2 * 3 * 3 , 2 * 2 * 2 * 3 , 3 * 2 * 5
→ 2⁴ * 3² * 5.
→ 720.
_______________
Now, Let
Dividend = The least number of 7 digits.
Divisior = 720.
720 ) 1000000 ( 1388
720
_________
2800
2166
__________
6400
5760
___________
6400
5760
__________
640
So, We can write as, The least number of 7 digits = 1000000.
Required number is 1000000 + ( Divisior - Remainder )
→ 1,000,000 + ( 720 - 640 )
→ 1,000,000 + ( 80 )
→ 1,000,080.
________________________________
VerificatioN :
N1 = 16.
Let check N1 is exactly divisible by 1,000,080
→ 1,000,080 / N1
→ 1,000,080 / 16
→ 62,505.
__________________
N2 = 18.
→ 1,000,080 / N2
→ → 1,000,080 / 18
→ 55,560.
__________________
N3 = 24.
→ 1,000,080 / N3
→ → 1,000,080 / 24
→ 41,670.
__________________
N4 = 30.
→ 1,000,080 / N4
→ → 1,000,080 / 30
→ 33,336.
Therefore, the value of 7 least digits number that is exactly divisible by 16,18,24 and 30 is 1,000,080.
Step-by-step explanation: