Least Common Multiple (LCM) of 150 and 31
The least common multiple (LCM) of 150 and 31 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 150 and 31?
First, calculate the GCD of 150 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 31 = 4 remainder 26 |
| 2 | 31 ÷ 26 = 1 remainder 5 |
| 3 | 26 ÷ 5 = 5 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 31 | 2542 |
| 118 and 89 | 10502 |
| 29 and 169 | 4901 |
| 133 and 145 | 19285 |
| 142 and 103 | 14626 |