Least Common Multiple (LCM) of 31 and 91
The least common multiple (LCM) of 31 and 91 is 2821.
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 91?
First, calculate the GCD of 31 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 91 = 0 remainder 31 |
| 2 | 91 ÷ 31 = 2 remainder 29 |
| 3 | 31 ÷ 29 = 1 remainder 2 |
| 4 | 29 ÷ 2 = 14 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 99 | 4950 |
| 12 and 121 | 1452 |
| 70 and 196 | 980 |
| 62 and 108 | 3348 |
| 17 and 85 | 85 |