Question

math journal write two different whole numbers that have 6 as their greatest common factor. explain how you found your two numbers. then find the least common multiple of your numbers.

Explanation:

Step1: Recall the concept of GCF

The greatest - common factor (GCF) of two numbers is the largest number that divides both of them evenly. If the GCF of two numbers is 6, the two numbers must be multiples of 6.

Step2: Choose two pairs of numbers

Let's consider the pairs. One pair could be 6 and 12. The factors of 6 are 1, 2, 3, 6. The factors of 12 are 1, 2, 3, 4, 6, 12. The GCF of 6 and 12 is 6. Another pair could be 6 and 18. The factors of 18 are 1, 2, 3, 6, 9, 18. The GCF of 6 and 18 is 6.

Step3: Find the LCM

For the pair 6 and 12:
The multiples of 6 are 6, 12, 18, 24, …
The multiples of 12 are 12, 24, 36, …
The least - common multiple (LCM) of 6 and 12 is 12.
For the pair 6 and 18:
The multiples of 6 are 6, 12, 18, 24, …
The multiples of 18 are 18, 36, 54, …
The LCM of 6 and 18 is 18.

Answer:

Pair 1: 6 and 12, GCF = 6, LCM = 12
Pair 2: 6 and 18, GCF = 6, LCM = 18