Least Common Multiple (LCM) of 109 and 45
The least common multiple (LCM) of 109 and 45 is 4905.
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 109 and 45?
First, calculate the GCD of 109 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 45 = 2 remainder 19 |
| 2 | 45 ÷ 19 = 2 remainder 7 |
| 3 | 19 ÷ 7 = 2 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 |
|---|---|
| 57 and 125 | 7125 |
| 107 and 102 | 10914 |
| 168 and 10 | 840 |
| 153 and 19 | 2907 |
| 58 and 79 | 4582 |