Least Common Multiple (LCM) of 71 and 145
The least common multiple (LCM) of 71 and 145 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 71 and 145?
First, calculate the GCD of 71 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 145 = 0 remainder 71 |
| 2 | 145 ÷ 71 = 2 remainder 3 |
| 3 | 71 ÷ 3 = 23 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 140 | 420 |
| 160 and 99 | 15840 |
| 112 and 146 | 8176 |
| 174 and 191 | 33234 |
| 185 and 104 | 19240 |