Least Common Multiple (LCM) of 162 and 133
The least common multiple (LCM) of 162 and 133 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 162 and 133?
First, calculate the GCD of 162 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 133 = 1 remainder 29 |
| 2 | 133 ÷ 29 = 4 remainder 17 |
| 3 | 29 ÷ 17 = 1 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 172 | 20812 |
| 51 and 153 | 153 |
| 127 and 131 | 16637 |
| 114 and 79 | 9006 |
| 119 and 102 | 714 |