Least Common Multiple (LCM) of 31 and 97
The least common multiple (LCM) of 31 and 97 is 3007.
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 31 and 97?
First, calculate the GCD of 31 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 97 = 0 remainder 31 |
| 2 | 97 ÷ 31 = 3 remainder 4 |
| 3 | 31 ÷ 4 = 7 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 82 | 1394 |
| 137 and 135 | 18495 |
| 66 and 150 | 1650 |
| 25 and 106 | 2650 |
| 108 and 167 | 18036 |