How many numbers upto 450 are divisible by 4,6,8
To find out how many numbers up to 450 are divisible by 4, 6, and 8, we need to determine the least common multiple (LCM) of 4, 6, and 8. The LCM of three numbers is the smallest number that is divisible by all three of them.
To calculate the LCM of 4, 6, and 8, we can follow these steps:
Step 1: Find the prime factors of each number:
- Prime factors of 4: 2 * 2
- Prime factors of 6: 2 * 3
- Prime factors of 8: 2 * 2 * 2
Step 2: Determine the highest power of each prime factor:
- The highest power of 2 is 3 (from 8)
- The highest power of 3 is 1 (from 6)
Step 3: Multiply the prime factors raised to their highest power:
- Result: 2^3 * 3^1 = 8 * 3 = 24
Therefore, the LCM of 4, 6, and 8 is 24.
Now, to determine the count of numbers up to 450 that are divisible by 4, 6, and 8, we can divide 450 by 24.
450 ÷ 24 = 18 remainder 18
This means that there are 18 multiples of 24 up to 450. However, this count includes the number 450 itself, which is not less than 450. So we need to subtract 1 and get the final answer:
18 - 1 = 17
Hence, there are 17 numbers up to 450 that are divisible by 4, 6, and 8.
To determine the number of numbers up to 450 that are divisible by 4, 6, and 8, we need to find the least common multiple (LCM) of these three numbers.
First, let's find the LCM of 4 and 6:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
From the list above, we can see that the LCM of 4 and 6 is 12.
Now, let's find the LCM of 12 and 8:
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, ...
From the list above, we can see that the LCM of 12 and 8 is 24.
Therefore, the LCM of 4, 6, and 8 is 24.
To find the number of numbers up to 450 that are divisible by 4, 6, and 8, we can divide 450 by the LCM:
450 ÷ 24 = 18.75
Since we cannot have a fraction of a number, we need to round down to the nearest whole number.
Therefore, the number of numbers up to 450 that are divisible by 4, 6, and 8 is 18.