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.

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights