Least Common Multiple (LCM) of 156 and 189
The least common multiple (LCM) of 156 and 189 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 156 and 189?
First, calculate the GCD of 156 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 189 = 0 remainder 156 |
| 2 | 189 ÷ 156 = 1 remainder 33 |
| 3 | 156 ÷ 33 = 4 remainder 24 |
| 4 | 33 ÷ 24 = 1 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 36 | 900 |
| 174 and 21 | 1218 |
| 146 and 40 | 2920 |
| 97 and 86 | 8342 |
| 192 and 18 | 576 |