Least Common Multiple (LCM) of 78 and 177
The least common multiple (LCM) of 78 and 177 is 4602.
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 78 and 177?
First, calculate the GCD of 78 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 177 = 0 remainder 78 |
| 2 | 177 ÷ 78 = 2 remainder 21 |
| 3 | 78 ÷ 21 = 3 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 71 | 8023 |
| 65 and 67 | 4355 |
| 37 and 18 | 666 |
| 115 and 169 | 19435 |
| 34 and 162 | 2754 |