Least Common Multiple (LCM) of 45 and 106
The least common multiple (LCM) of 45 and 106 is 4770.
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 45 and 106?
First, calculate the GCD of 45 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 106 = 0 remainder 45 |
| 2 | 106 ÷ 45 = 2 remainder 16 |
| 3 | 45 ÷ 16 = 2 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 21 | 189 |
| 21 and 197 | 4137 |
| 120 and 74 | 4440 |
| 24 and 116 | 696 |
| 82 and 129 | 10578 |