Least Common Multiple (LCM) of 189 and 169
The least common multiple (LCM) of 189 and 169 is 31941.
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 189 and 169?
First, calculate the GCD of 189 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 169 = 1 remainder 20 |
| 2 | 169 ÷ 20 = 8 remainder 9 |
| 3 | 20 ÷ 9 = 2 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 104 | 312 |
| 71 and 42 | 2982 |
| 30 and 57 | 570 |
| 45 and 53 | 2385 |
| 15 and 128 | 1920 |