Least Common Multiple (LCM) of 189 and 88
The least common multiple (LCM) of 189 and 88 is 16632.
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 88?
First, calculate the GCD of 189 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 88 = 2 remainder 13 |
| 2 | 88 ÷ 13 = 6 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 117 | 8190 |
| 68 and 193 | 13124 |
| 140 and 133 | 2660 |
| 86 and 89 | 7654 |
| 71 and 165 | 11715 |