Least Common Multiple (LCM) of 67 and 164
The least common multiple (LCM) of 67 and 164 is 10988.
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 67 and 164?
First, calculate the GCD of 67 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 164 = 0 remainder 67 |
| 2 | 164 ÷ 67 = 2 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 |
|---|---|
| 151 and 105 | 15855 |
| 180 and 122 | 10980 |
| 166 and 125 | 20750 |
| 131 and 16 | 2096 |
| 34 and 129 | 4386 |