Least Common Multiple (LCM) of 131 and 169
The least common multiple (LCM) of 131 and 169 is 22139.
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 131 and 169?
First, calculate the GCD of 131 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 169 = 0 remainder 131 |
| 2 | 169 ÷ 131 = 1 remainder 38 |
| 3 | 131 ÷ 38 = 3 remainder 17 |
| 4 | 38 ÷ 17 = 2 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 75 | 2175 |
| 98 and 154 | 1078 |
| 29 and 25 | 725 |
| 42 and 12 | 84 |
| 180 and 19 | 3420 |