Least Common Multiple (LCM) of 106 and 73
The least common multiple (LCM) of 106 and 73 is 7738.
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 73?
First, calculate the GCD of 106 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 73 = 1 remainder 33 |
| 2 | 73 ÷ 33 = 2 remainder 7 |
| 3 | 33 ÷ 7 = 4 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 191 | 4011 |
| 135 and 100 | 2700 |
| 144 and 159 | 7632 |
| 40 and 86 | 1720 |
| 186 and 29 | 5394 |