Least Common Multiple (LCM) of 73 and 106
The least common multiple (LCM) of 73 and 106 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 73 and 106?
First, calculate the GCD of 73 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 106 = 0 remainder 73 |
| 2 | 106 ÷ 73 = 1 remainder 33 |
| 3 | 73 ÷ 33 = 2 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 59 | 9794 |
| 65 and 185 | 2405 |
| 112 and 11 | 1232 |
| 49 and 162 | 7938 |
| 159 and 197 | 31323 |