Least Common Multiple (LCM) of 164 and 185
The least common multiple (LCM) of 164 and 185 is 30340.
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 185?
First, calculate the GCD of 164 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 185 = 0 remainder 164 |
| 2 | 185 ÷ 164 = 1 remainder 21 |
| 3 | 164 ÷ 21 = 7 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 12 | 192 |
| 161 and 138 | 966 |
| 87 and 40 | 3480 |
| 119 and 106 | 12614 |
| 39 and 106 | 4134 |