Least Common Multiple (LCM) of 138 and 61
The least common multiple (LCM) of 138 and 61 is 8418.
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 61?
First, calculate the GCD of 138 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 61 = 2 remainder 16 |
| 2 | 61 ÷ 16 = 3 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 45 | 270 |
| 105 and 83 | 8715 |
| 188 and 54 | 5076 |
| 198 and 120 | 3960 |
| 87 and 17 | 1479 |