Least Common Multiple (LCM) of 24 and 34
The least common multiple (LCM) of 24 and 34 is 408.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 24 and 34?
First, calculate the GCD of 24 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 34 = 0 remainder 24 |
| 2 | 34 ÷ 24 = 1 remainder 10 |
| 3 | 24 ÷ 10 = 2 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 12 | 456 |
| 105 and 62 | 6510 |
| 117 and 112 | 13104 |
| 129 and 181 | 23349 |
| 69 and 174 | 4002 |