Least Common Multiple (LCM) of 169 and 200
The least common multiple (LCM) of 169 and 200 is 33800.
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 200?
First, calculate the GCD of 169 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 200 = 0 remainder 169 |
| 2 | 200 ÷ 169 = 1 remainder 31 |
| 3 | 169 ÷ 31 = 5 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 31 | 744 |
| 112 and 153 | 17136 |
| 41 and 186 | 7626 |
| 103 and 100 | 10300 |
| 92 and 88 | 2024 |