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 |
|---|---|
| 138 and 61 | 8418 |
| 48 and 196 | 2352 |
| 118 and 45 | 5310 |
| 113 and 130 | 14690 |
| 80 and 43 | 3440 |