Least Common Multiple (LCM) of 109 and 146
The least common multiple (LCM) of 109 and 146 is 15914.
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 109 and 146?
First, calculate the GCD of 109 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 146 = 0 remainder 109 |
| 2 | 146 ÷ 109 = 1 remainder 37 |
| 3 | 109 ÷ 37 = 2 remainder 35 |
| 4 | 37 ÷ 35 = 1 remainder 2 |
| 5 | 35 ÷ 2 = 17 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 34 | 3706 |
| 75 and 131 | 9825 |
| 138 and 176 | 12144 |
| 90 and 31 | 2790 |
| 106 and 110 | 5830 |