Least Common Multiple (LCM) of 117 and 46
The least common multiple (LCM) of 117 and 46 is 5382.
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 46?
First, calculate the GCD of 117 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 46 = 2 remainder 25 |
| 2 | 46 ÷ 25 = 1 remainder 21 |
| 3 | 25 ÷ 21 = 1 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 131 | 23580 |
| 96 and 88 | 1056 |
| 116 and 102 | 5916 |
| 147 and 39 | 1911 |
| 97 and 159 | 15423 |