Least Common Multiple (LCM) of 140 and 180
The least common multiple (LCM) of 140 and 180 is 1260.
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 180?
First, calculate the GCD of 140 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 180 = 0 remainder 140 |
| 2 | 180 ÷ 140 = 1 remainder 40 |
| 3 | 140 ÷ 40 = 3 remainder 20 |
| 4 | 40 ÷ 20 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 48 | 2832 |
| 60 and 58 | 1740 |
| 23 and 109 | 2507 |
| 60 and 61 | 3660 |
| 24 and 194 | 2328 |