Least Common Multiple (LCM) of 117 and 89
The least common multiple (LCM) of 117 and 89 is 10413.
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 89?
First, calculate the GCD of 117 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 89 = 1 remainder 28 |
| 2 | 89 ÷ 28 = 3 remainder 5 |
| 3 | 28 ÷ 5 = 5 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 120 | 17160 |
| 175 and 107 | 18725 |
| 93 and 21 | 651 |
| 124 and 137 | 16988 |
| 32 and 156 | 1248 |