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
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
2645
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:
1800
Write true (T) or false (F) for the following statement.
There are fourteen square number upto 200.
Find the square rootthe following by prime factorization.
11664
Find the square root the following by prime factorization.
190969
Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.
Find the least square number, exactly divisible by each one of the number:
8, 12, 15 and 20
Write the prime factorization of the following number and hence find their square root.
7744
By splitting into prime factors, find the square root of 194481.
A square board has an area of 144 square units. How long is each side of the board?
