Least Common Multiple (LCM) of 142 and 91
The least common multiple (LCM) of 142 and 91 is 12922.
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 91?
First, calculate the GCD of 142 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 91 = 1 remainder 51 |
| 2 | 91 ÷ 51 = 1 remainder 40 |
| 3 | 51 ÷ 40 = 1 remainder 11 |
| 4 | 40 ÷ 11 = 3 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 146 | 1606 |
| 190 and 96 | 9120 |
| 133 and 129 | 17157 |
| 10 and 68 | 340 |
| 189 and 196 | 5292 |