Least Common Multiple (LCM) of 138 and 155
The least common multiple (LCM) of 138 and 155 is 21390.
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 155?
First, calculate the GCD of 138 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 155 = 0 remainder 138 |
| 2 | 155 ÷ 138 = 1 remainder 17 |
| 3 | 138 ÷ 17 = 8 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 55 | 10010 |
| 181 and 73 | 13213 |
| 42 and 189 | 378 |
| 112 and 140 | 560 |
| 168 and 97 | 16296 |