Least Common Multiple (LCM) of 31 and 22
The least common multiple (LCM) of 31 and 22 is 682.
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 22?
First, calculate the GCD of 31 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 22 = 1 remainder 9 |
| 2 | 22 ÷ 9 = 2 remainder 4 |
| 3 | 9 ÷ 4 = 2 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 12 | 1500 |
| 130 and 101 | 13130 |
| 101 and 151 | 15251 |
| 102 and 171 | 5814 |
| 151 and 159 | 24009 |