Least Common Multiple (LCM) of 38 and 24
The least common multiple (LCM) of 38 and 24 is 456.
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 38 and 24?
First, calculate the GCD of 38 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 24 = 1 remainder 14 |
| 2 | 24 ÷ 14 = 1 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 12 | 276 |
| 24 and 114 | 456 |
| 53 and 60 | 3180 |
| 129 and 17 | 2193 |
| 149 and 56 | 8344 |