Least Common Multiple (LCM) of 133 and 162
The least common multiple (LCM) of 133 and 162 is 21546.
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 133 and 162?
First, calculate the GCD of 133 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 162 = 0 remainder 133 |
| 2 | 162 ÷ 133 = 1 remainder 29 |
| 3 | 133 ÷ 29 = 4 remainder 17 |
| 4 | 29 ÷ 17 = 1 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 63 | 11403 |
| 107 and 142 | 15194 |
| 165 and 100 | 3300 |
| 198 and 14 | 1386 |
| 192 and 50 | 4800 |