Least Common Multiple (LCM) of 17 and 100
The least common multiple (LCM) of 17 and 100 is 1700.
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 17 and 100?
First, calculate the GCD of 17 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 100 = 0 remainder 17 |
| 2 | 100 ÷ 17 = 5 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 117 | 2223 |
| 105 and 173 | 18165 |
| 87 and 43 | 3741 |
| 130 and 64 | 4160 |
| 139 and 102 | 14178 |