Determine the largest four digit number divisible by 18 , 25 , and 35

Answer 1

To find the largest four-digit number divisible by 18, 25, and 35, we need to find the least common multiple (LCM) of these three numbers.

First, we find the prime factorization of each number:

18 = 2 * 3^2
25 = 5^2
35 = 5 * 7

Next, we find the highest exponent for each prime factor:
- The number 18 has the highest exponent of 2 for the prime factor 2 and exponent of 1 for the prime factor 3.
- The number 25 has the highest exponent of 2 for the prime factor 5.
- The number 35 has the highest exponent of 1 for the prime factor 5 and exponent of 1 for the prime factor 7.

Now, we can determine the LCM by taking the product of the highest exponents of each prime factor:

LCM = 2^2 * 3^2 * 5^2 * 7 = 4 * 9 * 25 * 7 = 6300

Therefore, the largest four-digit number divisible by 18, 25, and 35 is 6300.