What is the shortest possible length of timber from which equal pieces of 24 cm and 36 cm can be cut?
24+36 = 60
That will give one of each.
not sure how 24 and 36 cm pieces can be equal, but LCM(24,36) = 72
72 cm is the shortest length that can be cut evenly into both 24- and 36-cm pieces
To find the shortest possible length of timber from which equal pieces of 24 cm and 36 cm can be cut, we need to find the least common multiple (LCM) of these two numbers.
The prime factorization of 24 is 2^3 * 3, while the prime factorization of 36 is 2^2 * 3^2.
To calculate the LCM, we need to take the highest power of each prime factor that appears in either number. So, the LCM can be calculated as:
LCM = 2^3 * 3^2 = 8 * 9 = 72 cm.
Therefore, the shortest possible length of timber from which equal pieces of 24 cm and 36 cm can be cut is 72 cm.
To find the shortest possible length of timber from which equal pieces of 24 cm and 36 cm can be cut, we need to find the least common multiple (LCM) of the two numbers.
Step 1: Prime factorize the two numbers.
- 24 = 2^3 * 3^1
- 36 = 2^2 * 3^2
Step 2: Identify the highest power of each prime factor.
- The highest power of 2 is 3.
- The highest power of 3 is 2.
Step 3: Multiply the highest powers of the prime factors.
- 2^3 * 3^2 = 8 * 9 = 72
Therefore, the LCM of 24 cm and 36 cm is 72 cm. This means that the shortest possible length of timber from which equal pieces of 24 cm and 36 cm can be cut is 72 cm.