Least Common Multiple (LCM) of 69 and 164
The least common multiple (LCM) of 69 and 164 is 11316.
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 69 and 164?
First, calculate the GCD of 69 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 164 = 0 remainder 69 |
| 2 | 164 ÷ 69 = 2 remainder 26 |
| 3 | 69 ÷ 26 = 2 remainder 17 |
| 4 | 26 ÷ 17 = 1 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 122 | 6222 |
| 15 and 31 | 465 |
| 119 and 161 | 2737 |
| 147 and 110 | 16170 |
| 76 and 159 | 12084 |