Least Common Multiple (LCM) of 169 and 199
The least common multiple (LCM) of 169 and 199 is 33631.
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 199?
First, calculate the GCD of 169 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 199 = 0 remainder 169 |
| 2 | 199 ÷ 169 = 1 remainder 30 |
| 3 | 169 ÷ 30 = 5 remainder 19 |
| 4 | 30 ÷ 19 = 1 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 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 |
|---|---|
| 37 and 137 | 5069 |
| 51 and 136 | 408 |
| 27 and 185 | 4995 |
| 45 and 115 | 1035 |
| 113 and 195 | 22035 |