Least Common Multiple (LCM) of 31 and 61
The least common multiple (LCM) of 31 and 61 is 1891.
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 61?
First, calculate the GCD of 31 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 61 = 0 remainder 31 |
| 2 | 61 ÷ 31 = 1 remainder 30 |
| 3 | 31 ÷ 30 = 1 remainder 1 |
| 4 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 83 | 2241 |
| 39 and 57 | 741 |
| 87 and 184 | 16008 |
| 61 and 52 | 3172 |
| 22 and 162 | 1782 |