Least Common Multiple (LCM) of 71 and 121
The least common multiple (LCM) of 71 and 121 is 8591.
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 121?
First, calculate the GCD of 71 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 121 = 0 remainder 71 |
| 2 | 121 ÷ 71 = 1 remainder 50 |
| 3 | 71 ÷ 50 = 1 remainder 21 |
| 4 | 50 ÷ 21 = 2 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 75 | 3975 |
| 165 and 120 | 1320 |
| 120 and 155 | 3720 |
| 44 and 84 | 924 |
| 100 and 194 | 9700 |