Least Common Multiple (LCM) of 31 and 62
The least common multiple (LCM) of 31 and 62 is 62.
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 62?
First, calculate the GCD of 31 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 62 = 0 remainder 31 |
| 2 | 62 ÷ 31 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 68 | 1428 |
| 117 and 67 | 7839 |
| 114 and 36 | 684 |
| 130 and 75 | 1950 |
| 54 and 14 | 378 |