Least Common Multiple (LCM) of 20 and 108
The least common multiple (LCM) of 20 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 20 and 108?
First, calculate the GCD of 20 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 108 = 0 remainder 20 |
| 2 | 108 ÷ 20 = 5 remainder 8 |
| 3 | 20 ÷ 8 = 2 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 65 | 8385 |
| 150 and 163 | 24450 |
| 98 and 105 | 1470 |
| 157 and 43 | 6751 |
| 70 and 108 | 3780 |