Least Common Multiple (LCM) of 45 and 108
The least common multiple (LCM) of 45 and 108 is 540.
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 108?
First, calculate the GCD of 45 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 108 = 0 remainder 45 |
| 2 | 108 ÷ 45 = 2 remainder 18 |
| 3 | 45 ÷ 18 = 2 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 181 | 20815 |
| 32 and 19 | 608 |
| 61 and 98 | 5978 |
| 49 and 10 | 490 |
| 18 and 48 | 144 |