Least Common Multiple (LCM) of 163 and 84
The least common multiple (LCM) of 163 and 84 is 13692.
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 163 and 84?
First, calculate the GCD of 163 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 84 = 1 remainder 79 |
| 2 | 84 ÷ 79 = 1 remainder 5 |
| 3 | 79 ÷ 5 = 15 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 48 | 816 |
| 47 and 163 | 7661 |
| 165 and 22 | 330 |
| 20 and 45 | 180 |
| 89 and 137 | 12193 |