Least Common Multiple (LCM) of 188 and 77
The least common multiple (LCM) of 188 and 77 is 14476.
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 188 and 77?
First, calculate the GCD of 188 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 77 = 2 remainder 34 |
| 2 | 77 ÷ 34 = 2 remainder 9 |
| 3 | 34 ÷ 9 = 3 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 67 | 11457 |
| 39 and 28 | 1092 |
| 156 and 136 | 5304 |
| 38 and 155 | 5890 |
| 159 and 157 | 24963 |