Least Common Multiple (LCM) of 68 and 177
The least common multiple (LCM) of 68 and 177 is 12036.
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 68 and 177?
First, calculate the GCD of 68 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 177 = 0 remainder 68 |
| 2 | 177 ÷ 68 = 2 remainder 41 |
| 3 | 68 ÷ 41 = 1 remainder 27 |
| 4 | 41 ÷ 27 = 1 remainder 14 |
| 5 | 27 ÷ 14 = 1 remainder 13 |
| 6 | 14 ÷ 13 = 1 remainder 1 |
| 7 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 108 | 108 |
| 156 and 142 | 11076 |
| 184 and 149 | 27416 |
| 73 and 56 | 4088 |
| 91 and 40 | 3640 |