Least Common Multiple (LCM) of 106 and 71
The least common multiple (LCM) of 106 and 71 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 106 and 71?
First, calculate the GCD of 106 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 71 = 1 remainder 35 |
| 2 | 71 ÷ 35 = 2 remainder 1 |
| 3 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 90 | 7740 |
| 173 and 139 | 24047 |
| 191 and 57 | 10887 |
| 112 and 36 | 1008 |
| 127 and 61 | 7747 |