Least Common Multiple (LCM) of 29 and 71
The least common multiple (LCM) of 29 and 71 is 2059.
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 29 and 71?
First, calculate the GCD of 29 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 71 = 0 remainder 29 |
| 2 | 71 ÷ 29 = 2 remainder 13 |
| 3 | 29 ÷ 13 = 2 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 35 | 70 |
| 123 and 197 | 24231 |
| 51 and 43 | 2193 |
| 200 and 78 | 7800 |
| 102 and 39 | 1326 |