Least Common Multiple (LCM) of 189 and 117
The least common multiple (LCM) of 189 and 117 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 189 and 117?
First, calculate the GCD of 189 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 117 = 1 remainder 72 |
| 2 | 117 ÷ 72 = 1 remainder 45 |
| 3 | 72 ÷ 45 = 1 remainder 27 |
| 4 | 45 ÷ 27 = 1 remainder 18 |
| 5 | 27 ÷ 18 = 1 remainder 9 |
| 6 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 170 | 8160 |
| 77 and 123 | 9471 |
| 83 and 167 | 13861 |
| 80 and 139 | 11120 |
| 76 and 61 | 4636 |