Least Common Multiple (LCM) of 117 and 162
The least common multiple (LCM) of 117 and 162 is 2106.
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 162?
First, calculate the GCD of 117 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 162 = 0 remainder 117 |
| 2 | 162 ÷ 117 = 1 remainder 45 |
| 3 | 117 ÷ 45 = 2 remainder 27 |
| 4 | 45 ÷ 27 = 1 remainder 18 |
| 5 | 27 ÷ 18 = 1 remainder 9 |
| 6 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 194 | 14550 |
| 100 and 195 | 3900 |
| 49 and 175 | 1225 |
| 11 and 75 | 825 |
| 182 and 134 | 12194 |