Least Common Multiple (LCM) of 177 and 135
The least common multiple (LCM) of 177 and 135 is 7965.
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 177 and 135?
First, calculate the GCD of 177 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 135 = 1 remainder 42 |
| 2 | 135 ÷ 42 = 3 remainder 9 |
| 3 | 42 ÷ 9 = 4 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 76 | 3420 |
| 140 and 168 | 840 |
| 164 and 54 | 4428 |
| 106 and 37 | 3922 |
| 165 and 97 | 16005 |