Least Common Multiple (LCM) of 31 and 139
The least common multiple (LCM) of 31 and 139 is 4309.
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 139?
First, calculate the GCD of 31 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 139 = 0 remainder 31 |
| 2 | 139 ÷ 31 = 4 remainder 15 |
| 3 | 31 ÷ 15 = 2 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 19 | 342 |
| 125 and 82 | 10250 |
| 45 and 159 | 2385 |
| 17 and 155 | 2635 |
| 152 and 190 | 760 |