Least Common Multiple (LCM) of 84 and 163
The least common multiple (LCM) of 84 and 163 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 84 and 163?
First, calculate the GCD of 84 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 163 = 0 remainder 84 |
| 2 | 163 ÷ 84 = 1 remainder 79 |
| 3 | 84 ÷ 79 = 1 remainder 5 |
| 4 | 79 ÷ 5 = 15 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 130 | 8320 |
| 116 and 76 | 2204 |
| 170 and 166 | 14110 |
| 168 and 98 | 1176 |
| 13 and 145 | 1885 |