Least Common Multiple (LCM) of 138 and 149
The least common multiple (LCM) of 138 and 149 is 20562.
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 149?
First, calculate the GCD of 138 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 149 = 0 remainder 138 |
| 2 | 149 ÷ 138 = 1 remainder 11 |
| 3 | 138 ÷ 11 = 12 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 97 | 12901 |
| 149 and 42 | 6258 |
| 171 and 101 | 17271 |
| 173 and 102 | 17646 |
| 20 and 13 | 260 |