Least Common Multiple (LCM) of 108 and 90
The least common multiple (LCM) of 108 and 90 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 108 and 90?
First, calculate the GCD of 108 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 90 = 1 remainder 18 |
| 2 | 90 ÷ 18 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 42 | 1806 |
| 62 and 81 | 5022 |
| 123 and 78 | 3198 |
| 30 and 163 | 4890 |
| 11 and 179 | 1969 |