Least Common Multiple (LCM) of 138 and 77
The least common multiple (LCM) of 138 and 77 is 10626.
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 77?
First, calculate the GCD of 138 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 77 = 1 remainder 61 |
| 2 | 77 ÷ 61 = 1 remainder 16 |
| 3 | 61 ÷ 16 = 3 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 103 | 2163 |
| 117 and 176 | 20592 |
| 38 and 85 | 3230 |
| 118 and 82 | 4838 |
| 50 and 198 | 4950 |