What is the smallest whole number divisible by both 17 and 8?
Multiples of 17:
34, 51, 68, 85, 102, 119, 136, 153
Are any of those divisible by 8?
No
136
To find the smallest whole number divisible by both 17 and 8, we need to find the least common multiple (LCM) of these two numbers.
To calculate the LCM, we can use the prime factorization method.
1. Prime factorization of 17: 17 is a prime number, so its prime factorization is just 17 itself.
17 = 17^1
2. Prime factorization of 8: 8 can be written as the product of 2 raised to the power of 3.
8 = 2^3
3. Identify the common and uncommon prime factors:
Both 17 and 8 are prime factorized as 17^1 and 2^3, respectively. There are no common factors.
4. Multiply the common and uncommon prime factors:
Multiply 17^1 and 2^3 to get the LCM:
LCM(17, 8) = 17^1 * 2^3 = 136
Therefore, the smallest whole number divisible by both 17 and 8 is 136