Least Common Multiple (LCM) of 140 and 199
The least common multiple (LCM) of 140 and 199 is 27860.
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 199?
First, calculate the GCD of 140 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 199 = 0 remainder 140 |
| 2 | 199 ÷ 140 = 1 remainder 59 |
| 3 | 140 ÷ 59 = 2 remainder 22 |
| 4 | 59 ÷ 22 = 2 remainder 15 |
| 5 | 22 ÷ 15 = 1 remainder 7 |
| 6 | 15 ÷ 7 = 2 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 118 | 7670 |
| 120 and 160 | 480 |
| 140 and 149 | 20860 |
| 38 and 120 | 2280 |
| 111 and 37 | 111 |