Least Common Multiple (LCM) of 106 and 138
The least common multiple (LCM) of 106 and 138 is 7314.
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 106 and 138?
First, calculate the GCD of 106 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 138 = 0 remainder 106 |
| 2 | 138 ÷ 106 = 1 remainder 32 |
| 3 | 106 ÷ 32 = 3 remainder 10 |
| 4 | 32 ÷ 10 = 3 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 180 | 900 |
| 84 and 195 | 5460 |
| 169 and 50 | 8450 |
| 71 and 126 | 8946 |
| 158 and 87 | 13746 |