Least Common Multiple (LCM) of 114 and 140
The least common multiple (LCM) of 114 and 140 is 7980.
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 114 and 140?
First, calculate the GCD of 114 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 140 = 0 remainder 114 |
| 2 | 140 ÷ 114 = 1 remainder 26 |
| 3 | 114 ÷ 26 = 4 remainder 10 |
| 4 | 26 ÷ 10 = 2 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 157 | 1727 |
| 96 and 54 | 864 |
| 105 and 194 | 20370 |
| 157 and 112 | 17584 |
| 81 and 57 | 1539 |