Least Common Multiple (LCM) of 117 and 145
The least common multiple (LCM) of 117 and 145 is 16965.
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 145?
First, calculate the GCD of 117 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 145 = 0 remainder 117 |
| 2 | 145 ÷ 117 = 1 remainder 28 |
| 3 | 117 ÷ 28 = 4 remainder 5 |
| 4 | 28 ÷ 5 = 5 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 17 | 17 |
| 40 and 69 | 2760 |
| 19 and 159 | 3021 |
| 28 and 183 | 5124 |
| 121 and 199 | 24079 |