Least Common Multiple (LCM) of 117 and 189
The least common multiple (LCM) of 117 and 189 is 2457.
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 117 and 189?
First, calculate the GCD of 117 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 189 = 0 remainder 117 |
| 2 | 189 ÷ 117 = 1 remainder 72 |
| 3 | 117 ÷ 72 = 1 remainder 45 |
| 4 | 72 ÷ 45 = 1 remainder 27 |
| 5 | 45 ÷ 27 = 1 remainder 18 |
| 6 | 27 ÷ 18 = 1 remainder 9 |
| 7 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 82 | 1312 |
| 133 and 70 | 1330 |
| 33 and 143 | 429 |
| 147 and 146 | 21462 |
| 109 and 59 | 6431 |