Least Common Multiple (LCM) of 106 and 180
The least common multiple (LCM) of 106 and 180 is 9540.
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 180?
First, calculate the GCD of 106 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 180 = 0 remainder 106 |
| 2 | 180 ÷ 106 = 1 remainder 74 |
| 3 | 106 ÷ 74 = 1 remainder 32 |
| 4 | 74 ÷ 32 = 2 remainder 10 |
| 5 | 32 ÷ 10 = 3 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 178 | 33998 |
| 65 and 31 | 2015 |
| 105 and 72 | 2520 |
| 126 and 112 | 1008 |
| 38 and 20 | 380 |