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 |
|---|---|
| 138 and 182 | 12558 |
| 87 and 104 | 9048 |
| 145 and 192 | 27840 |
| 16 and 99 | 1584 |
| 148 and 14 | 1036 |