Least Common Multiple (LCM) of 108 and 60
The least common multiple (LCM) of 108 and 60 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 60?
First, calculate the GCD of 108 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 60 = 1 remainder 48 |
| 2 | 60 ÷ 48 = 1 remainder 12 |
| 3 | 48 ÷ 12 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 112 | 18480 |
| 136 and 144 | 2448 |
| 144 and 28 | 1008 |
| 51 and 30 | 510 |
| 185 and 81 | 14985 |