Least Common Multiple (LCM) of 189 and 156
The least common multiple (LCM) of 189 and 156 is 9828.
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 156?
First, calculate the GCD of 189 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 156 = 1 remainder 33 |
| 2 | 156 ÷ 33 = 4 remainder 24 |
| 3 | 33 ÷ 24 = 1 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 83 | 10624 |
| 159 and 145 | 23055 |
| 161 and 126 | 2898 |
| 143 and 163 | 23309 |
| 56 and 24 | 168 |