Least Common Multiple (LCM) of 108 and 30
The least common multiple (LCM) of 108 and 30 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 30?
First, calculate the GCD of 108 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 30 = 3 remainder 18 |
| 2 | 30 ÷ 18 = 1 remainder 12 |
| 3 | 18 ÷ 12 = 1 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 166 | 9296 |
| 125 and 70 | 1750 |
| 173 and 33 | 5709 |
| 91 and 58 | 5278 |
| 170 and 119 | 1190 |