Least Common Multiple (LCM) of 117 and 168
The least common multiple (LCM) of 117 and 168 is 6552.
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 168?
First, calculate the GCD of 117 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 168 = 0 remainder 117 |
| 2 | 168 ÷ 117 = 1 remainder 51 |
| 3 | 117 ÷ 51 = 2 remainder 15 |
| 4 | 51 ÷ 15 = 3 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 162 | 10530 |
| 162 and 178 | 14418 |
| 168 and 84 | 168 |
| 188 and 180 | 8460 |
| 31 and 128 | 3968 |