Least Common Multiple (LCM) of 109 and 131
The least common multiple (LCM) of 109 and 131 is 14279.
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 131?
First, calculate the GCD of 109 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 131 = 0 remainder 109 |
| 2 | 131 ÷ 109 = 1 remainder 22 |
| 3 | 109 ÷ 22 = 4 remainder 21 |
| 4 | 22 ÷ 21 = 1 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 56 | 1400 |
| 199 and 48 | 9552 |
| 14 and 32 | 224 |
| 191 and 188 | 35908 |
| 160 and 12 | 480 |