Least Common Multiple (LCM) of 132 and 165
The least common multiple (LCM) of 132 and 165 is 660.
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 165?
First, calculate the GCD of 132 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 165 = 0 remainder 132 |
| 2 | 165 ÷ 132 = 1 remainder 33 |
| 3 | 132 ÷ 33 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 34 | 1428 |
| 175 and 67 | 11725 |
| 40 and 43 | 1720 |
| 120 and 120 | 120 |
| 166 and 107 | 17762 |