Least Common Multiple (LCM) of 164 and 178
The least common multiple (LCM) of 164 and 178 is 14596.
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 178?
First, calculate the GCD of 164 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 178 = 0 remainder 164 |
| 2 | 178 ÷ 164 = 1 remainder 14 |
| 3 | 164 ÷ 14 = 11 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 98 | 1274 |
| 126 and 162 | 1134 |
| 194 and 158 | 15326 |
| 124 and 113 | 14012 |
| 155 and 65 | 2015 |