Least Common Multiple (LCM) of 71 and 133
The least common multiple (LCM) of 71 and 133 is 9443.
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 133?
First, calculate the GCD of 71 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 133 = 0 remainder 71 |
| 2 | 133 ÷ 71 = 1 remainder 62 |
| 3 | 71 ÷ 62 = 1 remainder 9 |
| 4 | 62 ÷ 9 = 6 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 42 | 2562 |
| 108 and 104 | 2808 |
| 80 and 188 | 3760 |
| 29 and 131 | 3799 |
| 59 and 127 | 7493 |