Least Common Multiple (LCM) of 117 and 65
The least common multiple (LCM) of 117 and 65 is 585.
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 65?
First, calculate the GCD of 117 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 65 = 1 remainder 52 |
| 2 | 65 ÷ 52 = 1 remainder 13 |
| 3 | 52 ÷ 13 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 24 | 648 |
| 112 and 80 | 560 |
| 31 and 95 | 2945 |
| 28 and 84 | 84 |
| 42 and 153 | 2142 |