Least Common Multiple (LCM) of 169 and 189
The least common multiple (LCM) of 169 and 189 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 169 and 189?
First, calculate the GCD of 169 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 189 = 0 remainder 169 |
| 2 | 189 ÷ 169 = 1 remainder 20 |
| 3 | 169 ÷ 20 = 8 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 58 | 2610 |
| 106 and 26 | 1378 |
| 54 and 106 | 2862 |
| 42 and 112 | 336 |
| 128 and 132 | 4224 |