Least Common Multiple (LCM) of 105 and 45
The least common multiple (LCM) of 105 and 45 is 315.
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 105 and 45?
First, calculate the GCD of 105 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 45 = 2 remainder 15 |
| 2 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 197 | 35657 |
| 39 and 132 | 1716 |
| 184 and 10 | 920 |
| 103 and 101 | 10403 |
| 177 and 119 | 21063 |