Least Common Multiple (LCM) of 108 and 146
The least common multiple (LCM) of 108 and 146 is 7884.
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 108 and 146?
First, calculate the GCD of 108 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 146 = 0 remainder 108 |
| 2 | 146 ÷ 108 = 1 remainder 38 |
| 3 | 108 ÷ 38 = 2 remainder 32 |
| 4 | 38 ÷ 32 = 1 remainder 6 |
| 5 | 32 ÷ 6 = 5 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 90 | 9810 |
| 110 and 71 | 7810 |
| 54 and 158 | 4266 |
| 165 and 96 | 5280 |
| 69 and 167 | 11523 |