Least Common Multiple (LCM) of 177 and 100
The least common multiple (LCM) of 177 and 100 is 17700.
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 177 and 100?
First, calculate the GCD of 177 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 100 = 1 remainder 77 |
| 2 | 100 ÷ 77 = 1 remainder 23 |
| 3 | 77 ÷ 23 = 3 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 37 | 3293 |
| 79 and 133 | 10507 |
| 196 and 157 | 30772 |
| 107 and 93 | 9951 |
| 200 and 13 | 2600 |