Least Common Multiple (LCM) of 71 and 164
The least common multiple (LCM) of 71 and 164 is 11644.
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 164?
First, calculate the GCD of 71 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 164 = 0 remainder 71 |
| 2 | 164 ÷ 71 = 2 remainder 22 |
| 3 | 71 ÷ 22 = 3 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 25 | 3200 |
| 119 and 146 | 17374 |
| 104 and 59 | 6136 |
| 11 and 56 | 616 |
| 196 and 15 | 2940 |