Least Common Multiple (LCM) of 20 and 38
The least common multiple (LCM) of 20 and 38 is 380.
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 20 and 38?
First, calculate the GCD of 20 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 38 = 0 remainder 20 |
| 2 | 38 ÷ 20 = 1 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 105 | 3360 |
| 84 and 54 | 756 |
| 170 and 128 | 10880 |
| 114 and 118 | 6726 |
| 114 and 66 | 1254 |