Answer:
The smallest perfect square that is exactly divisible by 10, 12, and 15 is 900.
Explanation:
The explanation is:
A perfect square is a number that is the product of two equal integers. For example, 25 is a perfect square because it is 5 times 5.
A number that is exactly divisible by 10, 12, and 15 must have all the prime factors of these numbers in its prime factorization. The prime factors of 10 are 2 and 5, the prime factors of 12 are 2 and 3, and the prime factors of 15 are 3 and 5. Therefore, the number must have at least two 2s, one 3, and one 5 in its prime factorization.
To make the number a perfect square, each prime factor must appear an even number of times. Therefore, we need to add another 2, another 3, and another 5 to the prime factorization. The number becomes 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5, which is equal to 900.
We can check that 900 is a perfect square by finding its square root. The square root of 900 is 30, which is an integer. We can also check that it is exactly divisible by 10, 12, and 15 by dividing it by these numbers. The quotients are all integers: 90, 75, and 60 respectively.