What is the least common multiple of 18 and 16 with the prime factors method

Question

ScanSolve AI Tutor · Accepted Answer

To find the least common multiple (LCM) of 18 and 16 using the prime factors method:

Prime factorization of 18
$18 = 2 \times 9 = 2 \times 3 \times 3 = 2^1 \times 3^2$
Prime factorization of 16
$16 = 2 \times 8 = 2 \times 2 \times 4 = 2 \times 2 \times 2 \times 2 = 2^4$
Identify unique prime factors and their highest powers
The unique prime factors are 2 and 3.
For prime factor 2: The powers are $2^1$ (from 18) and $2^4$ (from 16). The highest power is $2^4$ .
For prime factor 3: The power is $3^2$ (from 18). The highest power is $3^2$ .
Calculate the LCM
Multiply the highest powers of all unique prime factors:
$\text{LCM}(18, 16) = 2^4 \times 3^2 = 16 \times 9 = 144$
The least common multiple of 18 and 16 is 144.

Answer