Least Common Multiple (LCM) of 119 and 142
The least common multiple (LCM) of 119 and 142 is 16898.
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 142?
First, calculate the GCD of 119 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 142 = 0 remainder 119 |
| 2 | 142 ÷ 119 = 1 remainder 23 |
| 3 | 119 ÷ 23 = 5 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 108 | 2700 |
| 43 and 165 | 7095 |
| 48 and 172 | 2064 |
| 81 and 180 | 1620 |
| 108 and 164 | 4428 |