Find the least number which on decreasing by 20 is exactly divisible by 18,21,28 and 35
Answers
To find the least number which on decreasing by 20 is exactly divisible by 18,
21, 28, 35, first we have to take the L.C.M. of 18, 21, 28, 35
L.C.M. of 18, 21, 28, 35
_______________
2 | 18, 21, 28, 35
|_______________
2 | 9, 21, 14, 35
|_______________
3 | 9, 21, 7, 35
|_______________
3 | 3, 7, 7, 35
|_______________
5 | 1, 7, 7, 35
|_______________
7 | 1, 7, 7, 7
|_______________
| 1, 1, 1, 1
|
L.C.M. of 18, 21, 28, 35 = 2*2*3*3*5*7
= 1260
Now, the required number is 1260 + 20
= 1280
Therefore, 1280 is the least number which on decreasing by 20 is exactly divisible by 18, 21, 28, 35
Let us check it.
1280 - 20 = 1260
1) 1260 ÷ 18 = 70
2) 1260 ÷ 21 = 60
3) 1260 ÷ 28 = 45
4) 1260 ÷ 35 = 36
The answer is correct.
Answer
Solution - To fine the required least number, find the LCM of 18, 21, 28 and 35
2 I 18 21 28 35
-------I---------------------------------------------
2 I 9 21 14 35
------ I----------------------------------------------
3 I 9 21 7 35
------ I----------------------------------------------
3 I 3 7 7 35
------ I-----------------------------------------------
5 I 1 7 7 35
------ I----------------------------------------------
7 I 1 7 7 7
-------I---------------------------------------------
I 1 1 1 1
------- I---------------------------------------------
LCM = 2 * 2 * 3 * 3 * 5 * 7
= 1260
Therefore, required number = 1260 + 20 = 1280
Answer - 1280 is the least number which on decreasing by 20 is exactly divisible by 18,21,28 and 35
Check –
1280 – 20 = 1260
1260 / 18 = 70
1260 / 21 = 60
1260 / 28 = 45
1260 / 35 = 36
Number is divided exactly by 18, 21, 28 and 35.