Least Common Multiple (LCM) of 31 and 172
The least common multiple (LCM) of 31 and 172 is 5332.
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 172?
First, calculate the GCD of 31 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 172 = 0 remainder 31 |
| 2 | 172 ÷ 31 = 5 remainder 17 |
| 3 | 31 ÷ 17 = 1 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 103 | 17819 |
| 141 and 148 | 20868 |
| 72 and 187 | 13464 |
| 49 and 81 | 3969 |
| 200 and 191 | 38200 |