Least Common Multiple (LCM) of 71 and 106
The least common multiple (LCM) of 71 and 106 is 7526.
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 106?
First, calculate the GCD of 71 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 106 = 0 remainder 71 |
| 2 | 106 ÷ 71 = 1 remainder 35 |
| 3 | 71 ÷ 35 = 2 remainder 1 |
| 4 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 198 | 29502 |
| 105 and 87 | 3045 |
| 132 and 197 | 26004 |
| 13 and 85 | 1105 |
| 165 and 183 | 10065 |