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 |
|---|---|
| 72 and 197 | 14184 |
| 22 and 152 | 1672 |
| 157 and 69 | 10833 |
| 143 and 55 | 715 |
| 141 and 117 | 5499 |