Least Common Multiple (LCM) of 40 and 140
The least common multiple (LCM) of 40 and 140 is 280.
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 40 and 140?
First, calculate the GCD of 40 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 140 = 0 remainder 40 |
| 2 | 140 ÷ 40 = 3 remainder 20 |
| 3 | 40 ÷ 20 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 200 | 15400 |
| 153 and 58 | 8874 |
| 132 and 100 | 3300 |
| 84 and 71 | 5964 |
| 30 and 72 | 360 |