Least Common Multiple (LCM) of 31 and 117
The least common multiple (LCM) of 31 and 117 is 3627.
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 117?
First, calculate the GCD of 31 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 117 = 0 remainder 31 |
| 2 | 117 ÷ 31 = 3 remainder 24 |
| 3 | 31 ÷ 24 = 1 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 51 | 8925 |
| 11 and 129 | 1419 |
| 103 and 187 | 19261 |
| 86 and 184 | 7912 |
| 141 and 103 | 14523 |