Least Common Multiple (LCM) of 100 and 171
The least common multiple (LCM) of 100 and 171 is 17100.
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 171?
First, calculate the GCD of 100 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 171 = 0 remainder 100 |
| 2 | 171 ÷ 100 = 1 remainder 71 |
| 3 | 100 ÷ 71 = 1 remainder 29 |
| 4 | 71 ÷ 29 = 2 remainder 13 |
| 5 | 29 ÷ 13 = 2 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 176 | 7920 |
| 49 and 85 | 4165 |
| 117 and 31 | 3627 |
| 80 and 151 | 12080 |
| 150 and 78 | 1950 |