determine the largest number of four digits which is divisible by 18,25, and 35.
see related questions below
3150
To determine the largest number of four digits that is divisible by 18, 25, and 35, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest number that is divisible by all the given numbers.
First, we find the factors of each number:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 25: 1, 5, 25
Factors of 35: 1, 5, 7, 35
Next, we look for the highest power of each prime factor among the three numbers. In this case, the highest powers are:
2^1, 3^2, 5^2, 7^1
To find the LCM, we multiply all these highest powers together:
2^1 * 3^2 * 5^2 * 7^1 = 2 * 9 * 25 * 7 = 3150
Therefore, the largest number of four digits divisible by 18, 25, and 35 is 3150.