Find the lowest common multiple of the following

Question

84=2 squaredx3x7
56= 2 power of 3x7

Answer 1

To find the lowest common multiple (LCM) of two numbers, you should identify their prime factorization and then take the highest powers of all prime factors that appear in both factorizations.

Based on the provided factorizations:

84 = 2^2 × 3 × 7
56 = 2^3 × 7

Now, to determine the LCM, we will take the highest powers of each prime that appear in the factorizations. Here's the breakdown:

- For the prime number 2: The highest power in the provided factorizations is 2^3 (from 56).
- For the prime number 3: It only appears in the factorization of 84, as 3^1.
- For the prime number 7: It appears in both factorizations as 7^1, so we only need it once.

Putting it all together:

LCM = 2^3 × 3^1 × 7^1

Now calculate the LCM:

LCM = 8 × 3 × 7
LCM = 24 × 7
LCM = 168

Therefore, the lowest common multiple of 84 and 56 is 168.