Least Common Multiple (LCM) of 31 and 150
The least common multiple (LCM) of 31 and 150 is 4650.
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 150?
First, calculate the GCD of 31 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 150 = 0 remainder 31 |
| 2 | 150 ÷ 31 = 4 remainder 26 |
| 3 | 31 ÷ 26 = 1 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 122 | 14762 |
| 54 and 186 | 1674 |
| 150 and 83 | 12450 |
| 14 and 135 | 1890 |
| 133 and 155 | 20615 |