Least Common Multiple (LCM) of 39 and 138
The least common multiple (LCM) of 39 and 138 is 1794.
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 39 and 138?
First, calculate the GCD of 39 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 138 = 0 remainder 39 |
| 2 | 138 ÷ 39 = 3 remainder 21 |
| 3 | 39 ÷ 21 = 1 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 14 | 28 |
| 90 and 103 | 9270 |
| 64 and 122 | 3904 |
| 102 and 109 | 11118 |
| 117 and 31 | 3627 |