Least Common Multiple (LCM) of 109 and 71
The least common multiple (LCM) of 109 and 71 is 7739.
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 71?
First, calculate the GCD of 109 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 71 = 1 remainder 38 |
| 2 | 71 ÷ 38 = 1 remainder 33 |
| 3 | 38 ÷ 33 = 1 remainder 5 |
| 4 | 33 ÷ 5 = 6 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 160 | 160 |
| 199 and 57 | 11343 |
| 109 and 166 | 18094 |
| 32 and 58 | 928 |
| 117 and 89 | 10413 |