Least Common Multiple (LCM) of 145 and 171
The least common multiple (LCM) of 145 and 171 is 24795.
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 145 and 171?
First, calculate the GCD of 145 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 171 = 0 remainder 145 |
| 2 | 171 ÷ 145 = 1 remainder 26 |
| 3 | 145 ÷ 26 = 5 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 39 | 4134 |
| 30 and 186 | 930 |
| 82 and 54 | 2214 |
| 156 and 31 | 4836 |
| 42 and 170 | 3570 |