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 |
|---|---|
| 58 and 82 | 2378 |
| 28 and 111 | 3108 |
| 170 and 178 | 15130 |
| 51 and 195 | 3315 |
| 100 and 49 | 4900 |