Least Common Multiple (LCM) of 100 and 173
The least common multiple (LCM) of 100 and 173 is 17300.
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 173?
First, calculate the GCD of 100 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 173 = 0 remainder 100 |
| 2 | 173 ÷ 100 = 1 remainder 73 |
| 3 | 100 ÷ 73 = 1 remainder 27 |
| 4 | 73 ÷ 27 = 2 remainder 19 |
| 5 | 27 ÷ 19 = 1 remainder 8 |
| 6 | 19 ÷ 8 = 2 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 105 | 19320 |
| 69 and 69 | 69 |
| 98 and 181 | 17738 |
| 193 and 111 | 21423 |
| 68 and 124 | 2108 |