Least Common Multiple (LCM) of 189 and 72
The least common multiple (LCM) of 189 and 72 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 189 and 72?
First, calculate the GCD of 189 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 72 = 2 remainder 45 |
| 2 | 72 ÷ 45 = 1 remainder 27 |
| 3 | 45 ÷ 27 = 1 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 57 | 6954 |
| 19 and 20 | 380 |
| 199 and 40 | 7960 |
| 86 and 18 | 774 |
| 137 and 175 | 23975 |