Advertisements
Advertisements
Question
Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.
Advertisements
Solution
The number that will be perfectly divisible by each one of 4, 9, and 10 is their LCM. The LCM of these numbers is as follows:
| 2 | 4, 9, 10 |
| 2 | 2, 9, 5 |
| 3 | 1, 9, 5 |
| 3 | 1, 3, 5 |
| 5 | 1, 1, 5 |
| 1, 1, 1 |
LCM of 4, 9, 10 = 2 × 2 × 3 × 3 × 5 = 180
Here, prime factor 5 does not have its pair. Therefore, 180 is not a perfect square. If we multiply 180 with 5, then the number will become a perfect square. Therefore, 180 should be multiplied with 5 to obtain a perfect square.
Hence, the required square number is 180 × 5 = 900.
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.
252
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.
396
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 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.
The product of two numbers is 1296. If one number is 16 times the other, find the numbers.
Find the smallest number by which 12748 be mutliplied so that the product is a perfect square?
Examine if the following is a perfect square
190
Using prime factorisation, find which of the following are perfect squares.
841
Using prime factorisation, find the square roots of 4761
