Least Common Multiple (LCM) of 138 and 71
The least common multiple (LCM) of 138 and 71 is 9798.
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 71?
First, calculate the GCD of 138 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 71 = 1 remainder 67 |
| 2 | 71 ÷ 67 = 1 remainder 4 |
| 3 | 67 ÷ 4 = 16 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 94 | 8178 |
| 44 and 41 | 1804 |
| 72 and 188 | 3384 |
| 71 and 124 | 8804 |
| 117 and 75 | 2925 |