Least Common Multiple (LCM) of 162 and 117
The least common multiple (LCM) of 162 and 117 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 162 and 117?
First, calculate the GCD of 162 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 117 = 1 remainder 45 |
| 2 | 117 ÷ 45 = 2 remainder 27 |
| 3 | 45 ÷ 27 = 1 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 31 | 4278 |
| 125 and 40 | 1000 |
| 145 and 52 | 7540 |
| 102 and 106 | 5406 |
| 108 and 155 | 16740 |