(ii) Find the smallest number which, on being added 23 to it, is exactly divisible by 32, 36, 48 and 96.
(iii) Find the least length of a rope which can be cut into whole number of pieces of lengths 45 cm, 75 cm and 81 cm.
(iv) Find the greatest number of 4-digits which is exactly divisible by 40, 48 and 60.
(v) What is the least number of saplings that can be arranged in rows of 12, 15 or 40 in each row?
Answers
Solution :-
We have to find the smallest number which, on being added 23 to it, is exactly divisible by 32, 36, 48 and 96.
For it first we have to find the L.C.M. of 32, 36, 48 and 96 and then subtract 23 from it. After subtracting 23, the remaining number will be the required number.
L.C.M. of 32, 36, 48 and 96
_________________
2 | 32, 36, 48, 96
|________________
2 | 16, 18, 24, 48
|________________
2 | 8, 9, 12, 24
|________________
2 | 4, 9, 6, 12
|________________
2 | 2, 9, 3, 6
|________________
3 | 1, 9, 3, 3
|________________
3 | 1, 3, 1, 1
|________________
| 1, 1, 1, 1
|
L.C.M. = 2*2*2*2*2*3*3 = 288
Now, subtracting 23 from it -
288 - 23 = 265
265 is the required smallest number which, on being added 23 to it, is exactly divisible by 32, 36, 48 and 96.
Answer:
Molecule, a group of two or more atoms that form the smallest identifiable unit into which a pure substance can be divided and still retain the composition and chemical properties of that substance.
Step-by-step explanation:
Hi dear Army!
Can I have ur intro please?