Least Common Multiple (LCM) of 131 and 97
The least common multiple (LCM) of 131 and 97 is 12707.
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 97?
First, calculate the GCD of 131 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 97 = 1 remainder 34 |
| 2 | 97 ÷ 34 = 2 remainder 29 |
| 3 | 34 ÷ 29 = 1 remainder 5 |
| 4 | 29 ÷ 5 = 5 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 23 | 1679 |
| 158 and 62 | 4898 |
| 157 and 118 | 18526 |
| 197 and 24 | 4728 |
| 117 and 139 | 16263 |