Least Common Multiple (LCM) of 117 and 102
The least common multiple (LCM) of 117 and 102 is 3978.
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 102?
First, calculate the GCD of 117 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 102 = 1 remainder 15 |
| 2 | 102 ÷ 15 = 6 remainder 12 |
| 3 | 15 ÷ 12 = 1 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 12 | 204 |
| 193 and 106 | 20458 |
| 100 and 26 | 1300 |
| 174 and 17 | 2958 |
| 11 and 177 | 1947 |