Least Common Multiple (LCM) of 164 and 177
The least common multiple (LCM) of 164 and 177 is 29028.
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 177?
First, calculate the GCD of 164 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 177 = 0 remainder 164 |
| 2 | 177 ÷ 164 = 1 remainder 13 |
| 3 | 164 ÷ 13 = 12 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 47 | 2115 |
| 61 and 121 | 7381 |
| 145 and 161 | 23345 |
| 80 and 55 | 880 |
| 85 and 122 | 10370 |