Least Common Multiple (LCM) of 140 and 108
The least common multiple (LCM) of 140 and 108 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 140 and 108?
First, calculate the GCD of 140 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 108 = 1 remainder 32 |
| 2 | 108 ÷ 32 = 3 remainder 12 |
| 3 | 32 ÷ 12 = 2 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 15 | 285 |
| 36 and 44 | 396 |
| 66 and 46 | 1518 |
| 103 and 21 | 2163 |
| 40 and 71 | 2840 |