Least Common Multiple (LCM) of 145 and 117
The least common multiple (LCM) of 145 and 117 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 145 and 117?
First, calculate the GCD of 145 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 117 = 1 remainder 28 |
| 2 | 117 ÷ 28 = 4 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 |
|---|---|
| 85 and 117 | 9945 |
| 161 and 108 | 17388 |
| 113 and 168 | 18984 |
| 84 and 14 | 84 |
| 190 and 58 | 5510 |