Least Common Multiple (LCM) of 140 and 200
The least common multiple (LCM) of 140 and 200 is 1400.
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 200?
First, calculate the GCD of 140 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 200 = 0 remainder 140 |
| 2 | 200 ÷ 140 = 1 remainder 60 |
| 3 | 140 ÷ 60 = 2 remainder 20 |
| 4 | 60 ÷ 20 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 53 | 10282 |
| 185 and 92 | 17020 |
| 94 and 24 | 1128 |
| 104 and 112 | 1456 |
| 114 and 19 | 114 |