Next, we find the prime factorization of 36. We can express 36 as 2 × 18, then 2 × 2 × 9, and finally 2 × 2 × 3 × 3. In exponential form, this is 2² × 3².

Finally, we multiply these highest powers together to get the LCM. So, 2³ × 3² = 8 × 9 = 72. Therefore, the LCM of 24 and 36 is 72.

Find the LCM of 24 and 36 using prime factorisation

Answer: The LCM of 24 and 36 is 72.

Step-by-step solution

Step 1: Prime Factorization of 24

To find the Least Common Multiple (LCM) using prime factorization, we first need to express each number as a product of its prime factors. For the number 24, we can break it down into $2 \times 12$ , then $2 \times 2 \times 6$ , and finally $2 \times 2 \times 2 \times 3$ . This can be written in exponential form as $2^3 \times 3^1$ .

Step 2: Prime Factorization of 36

Next, we find the prime factorization of 36. We can express 36 as $2 \times 18$ , then $2 \times 2 \times 9$ , and finally $2 \times 2 \times 3 \times 3$ . In exponential form, this is $2^2 \times 3^2$ .

Step 3: Identify Highest Powers of Common Prime Factors

To find the LCM, we need to identify all unique prime factors from both numbers and take the highest power of each. For the prime factor 2, the highest power is $2^3$ (from 24). For the prime factor 3, the highest power is $3^2$ (from 36).

Step 4: Calculate the LCM

Finally, we multiply these highest powers together to get the LCM. So, $2^3 \times 3^2 = 8 \times 9 = 72$ . Therefore, the LCM of 24 and 36 is 72.

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