Least Common Multiple (LCM) of 31 and 122
The least common multiple (LCM) of 31 and 122 is 3782.
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 122?
First, calculate the GCD of 31 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 122 = 0 remainder 31 |
| 2 | 122 ÷ 31 = 3 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 |
|---|---|
| 20 and 145 | 580 |
| 140 and 128 | 4480 |
| 58 and 160 | 4640 |
| 124 and 94 | 5828 |
| 91 and 149 | 13559 |