Least Common Multiple (LCM) of 22 and 138
The least common multiple (LCM) of 22 and 138 is 1518.
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 22 and 138?
First, calculate the GCD of 22 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 138 = 0 remainder 22 |
| 2 | 138 ÷ 22 = 6 remainder 6 |
| 3 | 22 ÷ 6 = 3 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 177 | 5487 |
| 13 and 33 | 429 |
| 54 and 100 | 2700 |
| 187 and 171 | 31977 |
| 129 and 109 | 14061 |