Least Common Multiple (LCM) of 117 and 40
The least common multiple (LCM) of 117 and 40 is 4680.
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 40?
First, calculate the GCD of 117 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 40 = 2 remainder 37 |
| 2 | 40 ÷ 37 = 1 remainder 3 |
| 3 | 37 ÷ 3 = 12 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 15 | 330 |
| 57 and 34 | 1938 |
| 142 and 98 | 6958 |
| 46 and 67 | 3082 |
| 194 and 72 | 6984 |