Least Common Multiple (LCM) of 31 and 148
The least common multiple (LCM) of 31 and 148 is 4588.
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 148?
First, calculate the GCD of 31 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 148 = 0 remainder 31 |
| 2 | 148 ÷ 31 = 4 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 |
|---|---|
| 116 and 190 | 11020 |
| 31 and 10 | 310 |
| 89 and 187 | 16643 |
| 199 and 43 | 8557 |
| 31 and 85 | 2635 |