Least Common Multiple (LCM) of 100 and 177
The least common multiple (LCM) of 100 and 177 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 100 and 177?
First, calculate the GCD of 100 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 177 = 0 remainder 100 |
| 2 | 177 ÷ 100 = 1 remainder 77 |
| 3 | 100 ÷ 77 = 1 remainder 23 |
| 4 | 77 ÷ 23 = 3 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 160 | 960 |
| 168 and 198 | 5544 |
| 85 and 159 | 13515 |
| 177 and 149 | 26373 |
| 115 and 145 | 3335 |