Least Common Multiple (LCM) of 145 and 71
The least common multiple (LCM) of 145 and 71 is 10295.
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 71?
First, calculate the GCD of 145 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 71 = 2 remainder 3 |
| 2 | 71 ÷ 3 = 23 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 194 | 3298 |
| 25 and 45 | 225 |
| 191 and 177 | 33807 |
| 20 and 176 | 880 |
| 180 and 109 | 19620 |