Question

Find the LCM of the numbers 92 and 510.

Hint:

Take the highest powers of all prime factors from both numbers to find the LCM.

Answer 1

Step 1: Prime factorization.
\[ 92 = 2^2 \times 23 \] \[ 510 = 2 \times 3 \times 5 \times 17 \] Step 2: Take all unique prime factors with highest powers.
\[ \text{LCM} = 2^2 \times 3 \times 5 \times 17 \times 23 \] Step 3: Multiply.
\[ 4 \times 3 \times 5 \times 17 \times 23 = 23460 \] Step 4: Conclusion.
Hence, the LCM of 92 and 510 is 23460.