Least Common Multiple (LCM) of 162 and 107
The least common multiple (LCM) of 162 and 107 is 17334.
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 107?
First, calculate the GCD of 162 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 107 = 1 remainder 55 |
| 2 | 107 ÷ 55 = 1 remainder 52 |
| 3 | 55 ÷ 52 = 1 remainder 3 |
| 4 | 52 ÷ 3 = 17 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 180 | 3060 |
| 108 and 117 | 1404 |
| 16 and 59 | 944 |
| 102 and 30 | 510 |
| 165 and 177 | 9735 |