Least Common Multiple (LCM) of 108 and 140
The least common multiple (LCM) of 108 and 140 is 3780.
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 140?
First, calculate the GCD of 108 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 140 = 0 remainder 108 |
| 2 | 140 ÷ 108 = 1 remainder 32 |
| 3 | 108 ÷ 32 = 3 remainder 12 |
| 4 | 32 ÷ 12 = 2 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 166 | 6640 |
| 61 and 188 | 11468 |
| 147 and 167 | 24549 |
| 87 and 130 | 11310 |
| 168 and 13 | 2184 |