Least Common Multiple (LCM) of 31 and 46
The least common multiple (LCM) of 31 and 46 is 1426.
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 46?
First, calculate the GCD of 31 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 46 = 0 remainder 31 |
| 2 | 46 ÷ 31 = 1 remainder 15 |
| 3 | 31 ÷ 15 = 2 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 96 | 2784 |
| 21 and 16 | 336 |
| 112 and 149 | 16688 |
| 26 and 27 | 702 |
| 190 and 100 | 1900 |