Answer:
Product: 96
GCF: 4
LCM: 24
Product of the GCF and LCM: 96
Step-by-step explanation:
- Product - The answer to a multiplication problem.
- GCF - The greatest positive integer that evenly divides both numbers.
- LCM - The smallest multiple that both numbers have in common.
Now that we know what definitions are, we can solve this word problem.
12 × 8 = 96.
96 is the product.
To find the greatest common factor, we can list all of the factors for each number.
12: 1, 2, 3, 4, 6, 12
8: 1, 2, 4, 8
The largest factor both numbers have in common is 4.
Therefore, 4 is the greatest common factor.
To find the least common multiple, we can list the multiples of both numbers.
12: 12, 24, 36, 48, 60, 72, 84, 96
8: 8, 16, 24, 32, 40, 48, 56, 64
The smallest multiple both numbers have in common is 24.
Therefore, 24 is the least common multiple.
Lastly, we have to find the product of the GCF and the LCM.
The GCF is 4 and the LCM is 24.
4 × 24 = 96.
96 is the product.
Therefore, 96 is the product of the greatest common factor and the least common factor of 12 and 8.
