Least Common Multiple (LCM) of 88 and 189
The least common multiple (LCM) of 88 and 189 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 88 and 189?
First, calculate the GCD of 88 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 88 ÷ 189 = 0 remainder 88 |
| 2 | 189 ÷ 88 = 2 remainder 13 |
| 3 | 88 ÷ 13 = 6 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 34 | 510 |
| 107 and 129 | 13803 |
| 45 and 78 | 1170 |
| 143 and 38 | 5434 |
| 78 and 50 | 1950 |