Least Common Multiple (LCM) of 109 and 40
The least common multiple (LCM) of 109 and 40 is 4360.
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 40?
First, calculate the GCD of 109 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 40 = 2 remainder 29 |
| 2 | 40 ÷ 29 = 1 remainder 11 |
| 3 | 29 ÷ 11 = 2 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 159 | 159 |
| 102 and 40 | 2040 |
| 55 and 116 | 6380 |
| 155 and 183 | 28365 |
| 83 and 65 | 5395 |