Least Common Multiple (LCM) of 31 and 120
The least common multiple (LCM) of 31 and 120 is 3720.
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 120?
First, calculate the GCD of 31 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 120 = 0 remainder 31 |
| 2 | 120 ÷ 31 = 3 remainder 27 |
| 3 | 31 ÷ 27 = 1 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 24 | 312 |
| 198 and 33 | 198 |
| 157 and 187 | 29359 |
| 83 and 130 | 10790 |
| 84 and 125 | 10500 |