Least Common Multiple (LCM) of 137 and 142
The least common multiple (LCM) of 137 and 142 is 19454.
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 137 and 142?
First, calculate the GCD of 137 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 142 = 0 remainder 137 |
| 2 | 142 ÷ 137 = 1 remainder 5 |
| 3 | 137 ÷ 5 = 27 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 194 | 20758 |
| 153 and 41 | 6273 |
| 14 and 108 | 756 |
| 125 and 155 | 3875 |
| 52 and 18 | 468 |