For the numbers 10 and 12, what is the product of their greatest common factor and least common multiple?

To find the product of the greatest common factor (GCF) and the least common multiple (LCM) for the numbers 10 and 12, we first need to determine both values.

The GCF of two numbers is the largest number that divides both of them without leaving a remainder. For 10 and 12, the factors are:

• Factors of 10: 1, 2, 5, 10

• Factors of 12: 1, 2, 3, 4, 6, 12

The common factors are 1 and 2, making the GCF equal to 2.

Next, the LCM is the smallest number that both original numbers divide into without a remainder. To find the LCM, we can use the prime factorization method:

• Prime factorization of 10: 2 × 5

• Prime factorization of 12: 2^2 × 3

To compute the LCM, we take the highest power of each prime:

• Highest power of 2: 2^2 (from 12)

• Highest power of 3: 3^1 (from 12)

• Highest power of 5: