Directions: Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. In class, pairs of students were given numbers to work with. In each pair, one student found the greatest common factor and the
other student found the least common multiple.
Jess and Nate were given the numbers 8 and 12.
• Jess found that the greatest common factor is 4.
• Nate found that the least common multiple is 48.
One of these students made a mistake.
Which student made a mistake?
What number should the student have found instead?

Nate made a mistake. The LCM is actually 24.

Step-by-step explanation:

So, Jess found the GCF of 8 and 12 is 4. Let's make sure first.

Method 1: List the factors of 8 and 12.

8: 1, 2, 4, 8

12: 1, 2, 3, 4, 6, 12

Method 2: Or find the prime factorization of 8 and 12

8: 2 * 2 * 2

12: 2 * 2 * 3

Both 8 and 12 share 2 2's.

Multiply 2 by 2 to get 4 as the GCF

4 is the greatest factor 8 and 12 share, so Jess is correct.

Nate found the LCM of 8 and 12 is 48. Let's make sure that's correct.

Method 1: List the multiples of 8 and 12.

8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

24 is the smallest number 8 and 12 have in common.

Method 2: Union of Primes

8: 2 * 2 * 2

12 : 2 * 2 * 3

Create a union of these primes.

Union: 2 * 2 * 2 * 3

4 * 2 * 3

8 * 3

24 = LCM

The LCM of 8 and 12 is 24, not 48, so Nate is incorrect. Thus, Nate made the mistake.