Let's find the least square number other than zero which is divisible by 10,15,20and 30.Also let's write the next square number which will be divisible by these number.
To be a perfect square, the number must be factorable into pairs of equal factors
e.g. 144 = 2x2 x 2x2 x 3x3
10 = 2x5
15 = 3x5
20 = 2x2x5
30 = 2x3x5
So the LCM would be 2x2 x 3 x 5
So to pair them up, we will need another 3x5
So the least square divisible by 10,15,20, and 30
= 2x2 x 3x3 x 5x5 = 900
Using the ideas above, what do you think would be the answer to your second part ?
Well, let's dive into this mathematical circus and find the least square number that satisfies all the conditions. Let's break it down step by step, so even the clowns can follow along!
To find the least square number divisible by 10, 15, 20, and 30, we need to find the Least Common Multiple (LCM) of these numbers. The LCM of 10, 15, 20, and 30 is 60.
Now, let's find the smallest perfect square that is a multiple of 60. The smallest perfect square greater than 0 and divisible by 60 is 3600.
So, the least square number that satisfies all the given conditions is 3600.
Now, let's move on to the next square number divisible by 10, 15, 20, and 30. We know that the next square number will always be greater than the previous one, so we just need to find the smallest square number greater than 3600 that is divisible by 60.
And there you have it, ladies and gentlemen! The next square number divisible by 10, 15, 20, and 30, after 3600 is... *drumroll please*... 4900!
So, the next square number divisible by 10, 15, 20, and 30 is 4900.
I hope you enjoyed this mathematical circus performance! If you have any more questions or need further entertainment, feel free to ask!
To find the least square number divisible by 10, 15, 20, and 30, we need to find the least common multiple (LCM) of these numbers.
Step 1: Prime factorize the given numbers:
10 = 2 * 5
15 = 3 * 5
20 = 2^2 * 5
30 = 2 * 3 * 5
Step 2: Identify the highest power of each prime factor:
2^2 * 3 * 5
Step 3: Multiply the highest powers of each prime factor to find the LCM:
LCM = 2^2 * 3 * 5 = 60
So, the least square number divisible by 10, 15, 20, and 30 is 60^2 = 3600.
To find the next square number divisible by these numbers, we can find the next multiple of the LCM and then square it.
Next multiple of 60: 60 * 2 = 120
Next square number divisible by these numbers: 120^2 = 14400
Therefore, the next square number divisible by 10, 15, 20, and 30 is 14400.
To find the least square number that is divisible by a given set of numbers, we need to understand the concept of the least common multiple (LCM) of those numbers.
The LCM is the smallest positive integer that is divisible by each of the given numbers. In this case, the numbers are 10, 15, 20, and 30. We can find the LCM using the following steps:
Step 1: Factorize each number into its prime factors:
10 = 2 * 5
15 = 3 * 5
20 = 2^2 * 5
30 = 2 * 3 * 5
Step 2: Take the highest power of each prime factor:
For 2: the highest power is 2^2
For 3: the highest power is 3^1
For 5: the highest power is 5^1
Step 3: Multiply the highest powers of each prime factor:
2^2 * 3 * 5 = 60
Therefore, the LCM of 10, 15, 20, and 30 is 60.
Now, in order to find the least square number that is divisible by all these numbers, we need to find the smallest perfect square greater than or equal to 60.
The square root of 60 is approximately 7.75. So the next square number greater than or equal to 60 is 8^2 = 64.
Hence, the least square number (other than zero) divisible by 10, 15, 20, and 30 is 64, and the next square number divisible by these numbers is 64.