Least Common Multiple (LCM) of 67 and 178
The least common multiple (LCM) of 67 and 178 is 11926.
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 178?
First, calculate the GCD of 67 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 178 = 0 remainder 67 |
| 2 | 178 ÷ 67 = 2 remainder 44 |
| 3 | 67 ÷ 44 = 1 remainder 23 |
| 4 | 44 ÷ 23 = 1 remainder 21 |
| 5 | 23 ÷ 21 = 1 remainder 2 |
| 6 | 21 ÷ 2 = 10 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 140 | 1820 |
| 113 and 26 | 2938 |
| 168 and 192 | 1344 |
| 138 and 26 | 1794 |
| 87 and 117 | 3393 |