Least Common Multiple (LCM) of 138 and 163
The least common multiple (LCM) of 138 and 163 is 22494.
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 138 and 163?
First, calculate the GCD of 138 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 163 = 0 remainder 138 |
| 2 | 163 ÷ 138 = 1 remainder 25 |
| 3 | 138 ÷ 25 = 5 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 16 | 2032 |
| 143 and 24 | 3432 |
| 22 and 113 | 2486 |
| 107 and 123 | 13161 |
| 21 and 169 | 3549 |