Find the LCM of 24 and 28, 25 and 50, 32 and 24. Also find the LCM for 25 and 50.

Question

ScanSolve AI Tutor · Accepted Answer

First, let's check your answer for the LCM of 25 and 50.
Your method of listing multiples is correct:
Multiples of 25: 25, 50, 75, ...
Multiples of 50: 50, 100, ...
The least common multiple is 50.
✅ Correct!

Now, let's solve the other problems.

For 24 and 28:

Find the prime factorization of each number.
$24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1$ $28 = 2 \times 2 \times 7 = 2^2 \times 7^1$
Identify the highest power of each prime factor present in either factorization.
The prime factors are 2, 3, and 7.
The highest power of 2 is $2^3$ .
The highest power of 3 is $3^1$ .
The highest power of 7 is $7^1$ .
Multiply these highest powers together to find the LCM.
$\text{LCM}(24, 28) = 2^3 \times 3^1 \times 7^1 = 8 \times 3 \times 7 = 168$
The LCM of 24 and 28 is $\boxed{\text{168}}$ .

For 32 and 25:
Find the prime factorization of each number.
$32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5$ $25 = 5 \times 5 = 5^2$
Identify the highest power of each prime factor present in either factorization.
The prime factors are 2 and 5.
The highest power of 2 is $2^5$ .
The highest power of 5 is $5^2$ .
Multiply these highest powers together to find the LCM.
$\text{LCM}(32, 25) = 2^5 \times 5^2 = 32 \times 25 = 800$
The LCM of 32 and 25 is $\boxed{\text{800}}$ .

Find the LCM of 24 and 28, 25 and 50, 32 and 24. Also find the LCM for 25 and 50.

Answer

Step-by-step solution

Find the prime factorization of each number.

Identify the highest power of each prime factor present in either factorization.

Multiply these highest powers together to find the LCM.

Find the prime factorization of each number.

Identify the highest power of each prime factor present in either factorization.

Multiply these highest powers together to find the LCM.

Try one yourself

Still stuck on this one?

More Mathematics Questions