Least Common Multiple (LCM) of 132 and 162
The least common multiple (LCM) of 132 and 162 is 3564.
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 162?
First, calculate the GCD of 132 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 162 = 0 remainder 132 |
| 2 | 162 ÷ 132 = 1 remainder 30 |
| 3 | 132 ÷ 30 = 4 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 193 | 15054 |
| 16 and 150 | 1200 |
| 72 and 126 | 504 |
| 90 and 110 | 990 |
| 72 and 82 | 2952 |