Advertisements
Advertisements
प्रश्न
Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
Advertisements
उत्तर
Given: The least-square number which is exactly divisible by 8, 9 and 10 is equal to L.C.M. of 8, 9 and 10.
| 2 | 8, 9, 10 |
| 2 | 4, 9, 5 |
| 2 | 2, 9, 5 |
| 3 | 1, 9, 5 |
| 3 | 1, 3, 5 |
| 5 | 1, 1, 5 |
| 1, 1, 1 |
Hence, their L.C.M. is 2 × 2 × 2 × 3 × 3 × 5 = 360
As we see, (2 × 2) × 2 × (3 × 3) × 5
i.e. 2 and 5 is not able to make their pair.
Hence, to make it perfect square, it must be multiplied with 2 × 5 = 10
As, 360 × 10 = 3600
Hence, 3600 is least square number which is exactly divisible by 8, 9 and 10.
APPEARS IN
संबंधित प्रश्न
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
252
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:
2904
Write five numbers for which you cannot decide whether they are squares.
Write five numbers which you cannot decide whether they are square just by looking at the unit's digit.
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
25
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
71
Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.
Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
Find the square root by prime factorisation method
256
Find the least square number which is exactly divisible by 3, 4, 5, 6 and 8.
