Least Common Multiple (LCM) of 31 and 136
The least common multiple (LCM) of 31 and 136 is 4216.
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 136?
First, calculate the GCD of 31 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 136 = 0 remainder 31 |
| 2 | 136 ÷ 31 = 4 remainder 12 |
| 3 | 31 ÷ 12 = 2 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 107 | 17120 |
| 197 and 78 | 15366 |
| 47 and 179 | 8413 |
| 189 and 127 | 24003 |
| 92 and 52 | 1196 |