Least Common Multiple (LCM) of 173 and 100
The least common multiple (LCM) of 173 and 100 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 173 and 100?
First, calculate the GCD of 173 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 100 = 1 remainder 73 |
| 2 | 100 ÷ 73 = 1 remainder 27 |
| 3 | 73 ÷ 27 = 2 remainder 19 |
| 4 | 27 ÷ 19 = 1 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 109 | 12426 |
| 36 and 72 | 72 |
| 148 and 78 | 5772 |
| 183 and 13 | 2379 |
| 161 and 86 | 13846 |