Least Common Multiple (LCM) of 97 and 131
The least common multiple (LCM) of 97 and 131 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 97 and 131?
First, calculate the GCD of 97 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 131 = 0 remainder 97 |
| 2 | 131 ÷ 97 = 1 remainder 34 |
| 3 | 97 ÷ 34 = 2 remainder 29 |
| 4 | 34 ÷ 29 = 1 remainder 5 |
| 5 | 29 ÷ 5 = 5 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 111 | 11433 |
| 163 and 137 | 22331 |
| 45 and 58 | 2610 |
| 111 and 58 | 6438 |
| 40 and 168 | 840 |