Least Common Multiple (LCM) of 67 and 158
The least common multiple (LCM) of 67 and 158 is 10586.
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 67 and 158?
First, calculate the GCD of 67 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 158 = 0 remainder 67 |
| 2 | 158 ÷ 67 = 2 remainder 24 |
| 3 | 67 ÷ 24 = 2 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 128 | 10368 |
| 191 and 123 | 23493 |
| 59 and 181 | 10679 |
| 75 and 42 | 1050 |
| 189 and 48 | 3024 |