Least Common Multiple (LCM) of 132 and 163
The least common multiple (LCM) of 132 and 163 is 21516.
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 163?
First, calculate the GCD of 132 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 163 = 0 remainder 132 |
| 2 | 163 ÷ 132 = 1 remainder 31 |
| 3 | 132 ÷ 31 = 4 remainder 8 |
| 4 | 31 ÷ 8 = 3 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 106 | 4240 |
| 120 and 130 | 1560 |
| 53 and 150 | 7950 |
| 21 and 102 | 714 |
| 96 and 25 | 2400 |