Least Common Multiple (LCM) of 140 and 114
The least common multiple (LCM) of 140 and 114 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 140 and 114?
First, calculate the GCD of 140 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 114 = 1 remainder 26 |
| 2 | 114 ÷ 26 = 4 remainder 10 |
| 3 | 26 ÷ 10 = 2 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 190 | 23370 |
| 172 and 147 | 25284 |
| 10 and 55 | 110 |
| 60 and 35 | 420 |
| 70 and 128 | 4480 |