Least Common Multiple (LCM) of 119 and 140
The least common multiple (LCM) of 119 and 140 is 2380.
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 119 and 140?
First, calculate the GCD of 119 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 140 = 0 remainder 119 |
| 2 | 140 ÷ 119 = 1 remainder 21 |
| 3 | 119 ÷ 21 = 5 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 52 | 2080 |
| 198 and 141 | 9306 |
| 10 and 89 | 890 |
| 90 and 132 | 1980 |
| 169 and 175 | 29575 |