Least Common Multiple (LCM) of 169 and 185
The least common multiple (LCM) of 169 and 185 is 31265.
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 169 and 185?
First, calculate the GCD of 169 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 185 = 0 remainder 169 |
| 2 | 185 ÷ 169 = 1 remainder 16 |
| 3 | 169 ÷ 16 = 10 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 30 | 3210 |
| 65 and 103 | 6695 |
| 101 and 85 | 8585 |
| 138 and 174 | 4002 |
| 200 and 102 | 10200 |