Least Common Multiple (LCM) of 31 and 50
The least common multiple (LCM) of 31 and 50 is 1550.
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 50?
First, calculate the GCD of 31 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 50 = 0 remainder 31 |
| 2 | 50 ÷ 31 = 1 remainder 19 |
| 3 | 31 ÷ 19 = 1 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 46 | 1426 |
| 88 and 172 | 3784 |
| 141 and 169 | 23829 |
| 53 and 62 | 3286 |
| 138 and 180 | 4140 |