Least Common Multiple (LCM) of 118 and 189
The least common multiple (LCM) of 118 and 189 is 22302.
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 118 and 189?
First, calculate the GCD of 118 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 189 = 0 remainder 118 |
| 2 | 189 ÷ 118 = 1 remainder 71 |
| 3 | 118 ÷ 71 = 1 remainder 47 |
| 4 | 71 ÷ 47 = 1 remainder 24 |
| 5 | 47 ÷ 24 = 1 remainder 23 |
| 6 | 24 ÷ 23 = 1 remainder 1 |
| 7 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 150 | 2700 |
| 87 and 144 | 4176 |
| 89 and 76 | 6764 |
| 34 and 178 | 3026 |
| 46 and 161 | 322 |