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 |
|---|---|
| 144 and 70 | 5040 |
| 95 and 151 | 14345 |
| 123 and 143 | 17589 |
| 123 and 121 | 14883 |
| 184 and 58 | 5336 |