Least Common Multiple (LCM) of 180 and 77
The least common multiple (LCM) of 180 and 77 is 13860.
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 180 and 77?
First, calculate the GCD of 180 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 77 = 2 remainder 26 |
| 2 | 77 ÷ 26 = 2 remainder 25 |
| 3 | 26 ÷ 25 = 1 remainder 1 |
| 4 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 128 | 12928 |
| 137 and 15 | 2055 |
| 110 and 101 | 11110 |
| 110 and 192 | 10560 |
| 163 and 106 | 17278 |