Least Common Multiple (LCM) of 109 and 43
The least common multiple (LCM) of 109 and 43 is 4687.
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 43?
First, calculate the GCD of 109 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 43 = 2 remainder 23 |
| 2 | 43 ÷ 23 = 1 remainder 20 |
| 3 | 23 ÷ 20 = 1 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 14 | 434 |
| 114 and 37 | 4218 |
| 58 and 108 | 3132 |
| 27 and 178 | 4806 |
| 60 and 46 | 1380 |