Least Common Multiple (LCM) of 180 and 106
The least common multiple (LCM) of 180 and 106 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 180 and 106?
First, calculate the GCD of 180 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 106 = 1 remainder 74 |
| 2 | 106 ÷ 74 = 1 remainder 32 |
| 3 | 74 ÷ 32 = 2 remainder 10 |
| 4 | 32 ÷ 10 = 3 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 162 | 5022 |
| 144 and 122 | 8784 |
| 151 and 45 | 6795 |
| 118 and 29 | 3422 |
| 197 and 92 | 18124 |