Least Common Multiple (LCM) of 31 and 140
The least common multiple (LCM) of 31 and 140 is 4340.
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 140?
First, calculate the GCD of 31 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 140 = 0 remainder 31 |
| 2 | 140 ÷ 31 = 4 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 121 | 21175 |
| 128 and 58 | 3712 |
| 69 and 121 | 8349 |
| 10 and 193 | 1930 |
| 106 and 108 | 5724 |