Least Common Multiple (LCM) of 31 and 157
The least common multiple (LCM) of 31 and 157 is 4867.
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 157?
First, calculate the GCD of 31 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 157 = 0 remainder 31 |
| 2 | 157 ÷ 31 = 5 remainder 2 |
| 3 | 31 ÷ 2 = 15 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 51 | 5610 |
| 195 and 186 | 12090 |
| 170 and 131 | 22270 |
| 122 and 127 | 15494 |
| 68 and 75 | 5100 |