Determine the largest number of four digits which is divisible by 18,25,and 35
18 = 2 3^2
25 = 5^2
35 = 5 7
So, the LCM is 2 * 3^2 * 5^2 * 7 = 3150
3150*2 = 6300
3150*3 = 9450
I expect that is the largest 4-digit multiple.
If we decide 3150 with 18,25 and 35 so our question will be solved. 👍
9450
Find the largest number of 4 digits which is exactly divisible by 18,12 and 35
To find 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.
Step 1: Find the LCM of 18 and 25.
Prime factorize 18: 18 = 2 * 3 * 3
Prime factorize 25: 25 = 5 * 5
To find the LCM, we take the highest power of each prime factor that appears in either number. Therefore, the LCM of 18 and 25 is 2 * 3 * 3 * 5 * 5 = 450.
Step 2: Find the LCM of 450 and 35.
Prime factorize 450: 450 = 2 * 3 * 3 * 5 * 5
Prime factorize 35: 35 = 5 * 7
Again, taking the highest power of each prime factor that appears in either number, the LCM of 450 and 35 is 2 * 3 * 3 * 5 * 5 * 7 = 15750.
So, the largest number of four digits divisible by 18, 25, and 35 is 15,750.