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
Find the square root of the following number by the prime factorisation method.
5929
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.
252
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
7688
Find the square root the following by prime factorization.
4096
Find the square root the following by prime factorization.
24336
Find the square root the following by prime factorization.
190969
Write the prime factorization of the following number and hence find their square root.
9604
By splitting into prime factors, find the square root of 11025.
Find the smallest number by which 12748 be mutliplied so that the product is a perfect square?
Using prime factorisation, find which of the following are perfect squares.
11250
