Least Common Multiple (LCM) of 132 and 177
The least common multiple (LCM) of 132 and 177 is 7788.
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 132 and 177?
First, calculate the GCD of 132 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 177 = 0 remainder 132 |
| 2 | 177 ÷ 132 = 1 remainder 45 |
| 3 | 132 ÷ 45 = 2 remainder 42 |
| 4 | 45 ÷ 42 = 1 remainder 3 |
| 5 | 42 ÷ 3 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 60 | 1260 |
| 64 and 178 | 5696 |
| 155 and 56 | 8680 |
| 109 and 198 | 21582 |
| 48 and 172 | 2064 |