Least Common Multiple (LCM) of 31 and 145
The least common multiple (LCM) of 31 and 145 is 4495.
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 145?
First, calculate the GCD of 31 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 145 = 0 remainder 31 |
| 2 | 145 ÷ 31 = 4 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 49 | 8281 |
| 178 and 50 | 4450 |
| 66 and 55 | 330 |
| 115 and 34 | 3910 |
| 51 and 109 | 5559 |