Find the least number of piles so so that piles of 12, 15 and 20 marbles be made.
I think you mean least number of marbles.
12 = 2^2 * 3
15 = 3 * 5
20 = 2^2 * 5
So, the LCM is 2^2 * 3 * 5 = 60
60
Intelligent
Answer is 60
First we have to find the LCM of 12 , 15 and 20 . Then we have to multiply all the LCM and then we will get the answer, which is 60.
60 it can be
First if we find LCM of 12 15 and 20 by common division method and then multiply all the LCM then we will get our answer 60
I have one question can you give me the solution.
The question is this.
Find the smallest number which, when divided by 15,14,36 leave reminder as 7
To find the least number of piles such that piles of 12, 15, and 20 marbles can be made, we need to find the least common multiple (LCM) of these numbers.
One way to find the LCM is to list the multiples of each number and find the smallest number that is common to all three lists. However, this can be time-consuming.
An efficient way to find the LCM is by using prime factorization:
1. Prime factorize each number:
- 12 = 2^2 * 3
- 15 = 3 * 5
- 20 = 2^2 * 5
2. Write the prime factorization of each number with the highest powers of each prime:
- 12 = 2^2 * 3 * 5^0
- 15 = 2^0 * 3^1 * 5^1
- 20 = 2^2 * 3^0 * 5^1
3. Multiply the highest powers of each prime:
- 2^2 * 3^1 * 5^1 = 60
Therefore, the least number of piles required is 60.