Least Common Multiple (LCM) of 164 and 97
The least common multiple (LCM) of 164 and 97 is 15908.
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 164 and 97?
First, calculate the GCD of 164 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 97 = 1 remainder 67 |
| 2 | 97 ÷ 67 = 1 remainder 30 |
| 3 | 67 ÷ 30 = 2 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 128 | 1152 |
| 189 and 81 | 567 |
| 144 and 164 | 5904 |
| 136 and 144 | 2448 |
| 152 and 67 | 10184 |