Least Common Multiple (LCM) of 38 and 177
The least common multiple (LCM) of 38 and 177 is 6726.
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 38 and 177?
First, calculate the GCD of 38 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 177 = 0 remainder 38 |
| 2 | 177 ÷ 38 = 4 remainder 25 |
| 3 | 38 ÷ 25 = 1 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 39 | 5694 |
| 45 and 124 | 5580 |
| 131 and 80 | 10480 |
| 129 and 132 | 5676 |
| 31 and 135 | 4185 |