Least Common Multiple (LCM) of 142 and 194
The least common multiple (LCM) of 142 and 194 is 13774.
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 142 and 194?
First, calculate the GCD of 142 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 194 = 0 remainder 142 |
| 2 | 194 ÷ 142 = 1 remainder 52 |
| 3 | 142 ÷ 52 = 2 remainder 38 |
| 4 | 52 ÷ 38 = 1 remainder 14 |
| 5 | 38 ÷ 14 = 2 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 112 | 336 |
| 92 and 50 | 2300 |
| 106 and 18 | 954 |
| 40 and 176 | 880 |
| 108 and 36 | 108 |