Advertisements
Advertisements
Question
Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
Advertisements
Solution
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
RELATED QUESTIONS
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.
1458
Write true (T) or false (F) for the following statement.
No square number is negative.
Write true (T) or false (F) for the following statement .
There is no square number between 50 and 60.
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
25
Find the square rootthe following by prime factorization.
11664
Find the square root the following by prime factorization.
47089
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.
Out of 745 students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if 16 students were left out after the arrangement.
Examine if the following is a perfect square.
841
Using prime factorisation, find which of the following are perfect squares.
11250
