Least Common Multiple (LCM) of 140 and 162
The least common multiple (LCM) of 140 and 162 is 11340.
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 140 and 162?
First, calculate the GCD of 140 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 162 = 0 remainder 140 |
| 2 | 162 ÷ 140 = 1 remainder 22 |
| 3 | 140 ÷ 22 = 6 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 189 | 189 |
| 114 and 17 | 1938 |
| 83 and 85 | 7055 |
| 10 and 71 | 710 |
| 167 and 148 | 24716 |