Least Common Multiple (LCM) of 17 and 131
The least common multiple (LCM) of 17 and 131 is 2227.
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 17 and 131?
First, calculate the GCD of 17 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 131 = 0 remainder 17 |
| 2 | 131 ÷ 17 = 7 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 64 | 1344 |
| 106 and 34 | 1802 |
| 178 and 79 | 14062 |
| 181 and 42 | 7602 |
| 186 and 13 | 2418 |