Lcm of 24 and 8
The LCM (Least Common Multiple) of 24 and 8 is 24.
To find the least common multiple (LCM) of 24 and 8, we can use one of the following methods:
Method 1: Prime Factorization
1. Find the prime factorization of each number.
- The prime factorization of 24 is 2 * 2 * 2 * 3.
- The prime factorization of 8 is 2 * 2 * 2.
2. Identify the highest power of each prime factor that appears in either number.
- The highest power of 2 is 2 * 2 * 2, which is present in both numbers.
- The highest power of 3 is 3, which is only present in 24.
3. Multiply the highest powers together to find the LCM.
LCM = 2 * 2 * 2 * 3 = 8 * 3 = 24.
Therefore, the LCM of 24 and 8 is 24.
Method 2: Division Method
1. Begin by dividing the larger number (24) by the smaller number (8).
- 24 ÷ 8 = 3.
2. If the division is exact, the smaller number is the LCM. If not, continue to the next step.
3. Multiply the smaller number (8) by the next whole number (in this case, 2).
- 8 * 2 = 16.
4. Repeat step 1 using the new product (16) as the larger number and the original smaller number (8) as the divisor.
- 16 ÷ 8 = 2.
5. If the division is exact, the new product is the LCM. If not, repeat steps 3 and 4 until the division is exact.
In this case, after repeating steps 3 to 5 once more, we get:
- 8 * 3 = 24.
Therefore, the LCM of 24 and 8 is 24.