Answer:
8. 14
9. 720
Explanation:
Both questions are asking you to find the GCD (Greatest Common Divisor) and LCM (Lowest Common Multiple).
8. Find the greatest number that can divide 392 and 462 exactly.
Find the GCD of 392 and 462:
1. Find the prime factorization of 392
2^3 × 7^2 (2 × 2 × 2 × 7 × 7)
2. Find the prime factorization of 462
2 × 3 × 7 × 11
3. To find the GCD, multiply all prime factors common to all numbers
GCF = 2 × 7, therefore GCD = 14.
9. What is the smallest number that is divisible by 20, 48, and 72?
Find the LCM of 20, 48, and 72:
1. Find the prime factorization of 20
2^5 (2 × 2 × 5)
2. Find the prime factorization of 48
2^4 x 3 (2 × 2 × 2 × 2 × 3)
3. Find the prime factorization of 72
2^3 x 3^2 (2 × 2 × 2 × 3 × 3)
4. To find the LCM, multiply all prime factors
LCM = 2^4 × 3^2 × 5 (2 × 2 × 2 × 2 × 3 × 3 × 5), therefore GCF = 720
Calculator Input:
The easiest way to find the GCD or LCM of 2 or more numbers is by using a scientific calculator. Input GCD(x,y) or LCM(x,y) for the answer. This will work for any amount of numbers as long as the input is logical.
For questions 8 and 9, you would type in GCD(392,462) and LCM(20,48,72).
Not all calculators are made the same, so other labels might be GCF or HCF instead of GCD, and LCF instead of LCM. I use GCD and LCM because that's how it is on my calculator. There isn't any difference, so using any label is fine.