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 |
|---|---|
| 130 and 93 | 12090 |
| 153 and 48 | 2448 |
| 138 and 102 | 2346 |
| 54 and 177 | 3186 |
| 157 and 30 | 4710 |