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
12 = 2^2 * 3
15 = 3 * 5
20 = 2^2 * 5
So, the LCM is 2^2 * 3 * 5 = 60
The question is this.
Find the smallest number which, when divided by 15,14,36 leave reminder as 7
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.