Least Common Multiple (LCM) of 109 and 173
The least common multiple (LCM) of 109 and 173 is 18857.
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 109 and 173?
First, calculate the GCD of 109 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 173 = 0 remainder 109 |
| 2 | 173 ÷ 109 = 1 remainder 64 |
| 3 | 109 ÷ 64 = 1 remainder 45 |
| 4 | 64 ÷ 45 = 1 remainder 19 |
| 5 | 45 ÷ 19 = 2 remainder 7 |
| 6 | 19 ÷ 7 = 2 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 16 | 80 |
| 104 and 24 | 312 |
| 143 and 112 | 16016 |
| 53 and 107 | 5671 |
| 154 and 136 | 10472 |