Least Common Multiple (LCM) of 162 and 71
The least common multiple (LCM) of 162 and 71 is 11502.
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 71?
First, calculate the GCD of 162 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 71 = 2 remainder 20 |
| 2 | 71 ÷ 20 = 3 remainder 11 |
| 3 | 20 ÷ 11 = 1 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 133 | 19684 |
| 189 and 50 | 9450 |
| 143 and 75 | 10725 |
| 100 and 123 | 12300 |
| 190 and 21 | 3990 |