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 |
|---|---|
| 111 and 67 | 7437 |
| 78 and 38 | 1482 |
| 74 and 128 | 4736 |
| 39 and 123 | 1599 |
| 119 and 129 | 15351 |