Determine the largest four digit number divisible by 18 , 25 , and 35
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.
To determine the largest four-digit number divisible by 18, 25, and 35, we need to find the least common multiple (LCM) of these numbers.
To find the LCM, we can find the prime factorization of each number and then take the highest power of each prime factor:
Prime factorization of 18: 2 x 3^2
Prime factorization of 25: 5^2
Prime factorization of 35: 5 x 7
To find the LCM, we take the highest power of each prime factor:
2 x 3^2 x 5^2 x 7 = 2 x 9 x 25 x 7 = 3150
So, the largest four-digit number divisible by 18, 25, and 35 is 3150.