What is the smallest number that can be divided by 8 and 12 without a remainder?

Question

ScanSolve AI Tutor · Accepted Answer

To find the smallest number that can be divided by 8 and 12 without a remainder, we need to find the Least Common Multiple (LCM) of 8 and 12.

Find the prime factorization of each number.
$8 = 2 \times 2 \times 2 = 2^3$ $12 = 2 \times 2 \times 3 = 2^2 \times 3^1$
Identify all prime factors with their highest powers.
The prime factors are 2 and 3.
The highest power of 2 is $2^3$ (from 8).
The highest power of 3 is $3^1$ (from 12).
Multiply these highest powers together to find the LCM.
$\text{LCM}(8, 12) = 2^3 \times 3^1 = 8 \times 3 = 24$
The smallest number that can be divided by 8 and 12 without a remainder is $\boxed{\text{24}}$ .

Answer