Least Common Multiple (LCM) of 31 and 56
The least common multiple (LCM) of 31 and 56 is 1736.
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 56?
First, calculate the GCD of 31 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 56 = 0 remainder 31 |
| 2 | 56 ÷ 31 = 1 remainder 25 |
| 3 | 31 ÷ 25 = 1 remainder 6 |
| 4 | 25 ÷ 6 = 4 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 40 | 6440 |
| 196 and 108 | 5292 |
| 13 and 18 | 234 |
| 120 and 21 | 840 |
| 119 and 177 | 21063 |