Advertisements
Advertisements
प्रश्न
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
Advertisements
उत्तर
The number that is perfectly divisible by each of the numbers 8, 15, and 20 is their LCM.
| 2 | 8, 15, 20 |
| 2 | 4, 15, 10 |
| 2 | 2, 15, 5 |
| 3 | 1, 15, 5 |
| 5 | 1, 5, 5 |
| 1, 1, 1 |
LCM of 8, 15, and 20 = 2 × 2 × 2 × 3 × 5 = 120
Here, prime factors 2, 3, and 5 do not have their respective pairs. Therefore, 120 is not a perfect square.
Therefore, 120 should be multiplied by 2 × 3 × 5, i.e., 30, to obtain a perfect square.
Hence, the required square number is 120 × 2 × 3 × 5 = 3600
APPEARS IN
संबंधित प्रश्न
By just examining the unit digit, can you tell which of the following cannot be whole square?
1024
By just examining the unit digit, can you tell which of the following cannot be whole square?
1027
Write five numbers which you cannot decide whether they are square just by looking at the unit's digit.
Find the square root the following by prime factorization.
4096
Find the square root the following by prime factorization.
47089
The area of a square field is 5184 cm2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.
Find the least square number, exactly divisible by each one of the numbers:
(i) 6, 9, 15 and 20
Find the cube root of 729 and 6859 prime factorisation.
If `root(3)(1906624) xx sqrt(x)` = 3100, find x
Using prime factorisation, find the square roots of 4761
