Least Common Multiple (LCM) of 101 and 164
The least common multiple (LCM) of 101 and 164 is 16564.
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 101 and 164?
First, calculate the GCD of 101 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 164 = 0 remainder 101 |
| 2 | 164 ÷ 101 = 1 remainder 63 |
| 3 | 101 ÷ 63 = 1 remainder 38 |
| 4 | 63 ÷ 38 = 1 remainder 25 |
| 5 | 38 ÷ 25 = 1 remainder 13 |
| 6 | 25 ÷ 13 = 1 remainder 12 |
| 7 | 13 ÷ 12 = 1 remainder 1 |
| 8 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 125 | 12750 |
| 108 and 197 | 21276 |
| 189 and 49 | 1323 |
| 81 and 164 | 13284 |
| 162 and 111 | 5994 |