Least Common Multiple (LCM) of 72 and 189
The least common multiple (LCM) of 72 and 189 is 1512.
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 72 and 189?
First, calculate the GCD of 72 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 189 = 0 remainder 72 |
| 2 | 189 ÷ 72 = 2 remainder 45 |
| 3 | 72 ÷ 45 = 1 remainder 27 |
| 4 | 45 ÷ 27 = 1 remainder 18 |
| 5 | 27 ÷ 18 = 1 remainder 9 |
| 6 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 102 | 7242 |
| 186 and 159 | 9858 |
| 160 and 135 | 4320 |
| 198 and 116 | 11484 |
| 47 and 178 | 8366 |