Least Common Multiple (LCM) of 30 and 108
The least common multiple (LCM) of 30 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 30 and 108?
First, calculate the GCD of 30 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 108 = 0 remainder 30 |
| 2 | 108 ÷ 30 = 3 remainder 18 |
| 3 | 30 ÷ 18 = 1 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 135 | 2160 |
| 162 and 35 | 5670 |
| 141 and 123 | 5781 |
| 102 and 86 | 4386 |
| 41 and 37 | 1517 |