Least Common Multiple (LCM) of 120 and 177
The least common multiple (LCM) of 120 and 177 is 7080.
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 120 and 177?
First, calculate the GCD of 120 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 177 = 0 remainder 120 |
| 2 | 177 ÷ 120 = 1 remainder 57 |
| 3 | 120 ÷ 57 = 2 remainder 6 |
| 4 | 57 ÷ 6 = 9 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 55 | 6710 |
| 61 and 85 | 5185 |
| 10 and 112 | 560 |
| 105 and 65 | 1365 |
| 195 and 187 | 36465 |