Least Common Multiple (LCM) of 107 and 162
The least common multiple (LCM) of 107 and 162 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 107 and 162?
First, calculate the GCD of 107 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 162 = 0 remainder 107 |
| 2 | 162 ÷ 107 = 1 remainder 55 |
| 3 | 107 ÷ 55 = 1 remainder 52 |
| 4 | 55 ÷ 52 = 1 remainder 3 |
| 5 | 52 ÷ 3 = 17 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 47 | 5969 |
| 129 and 159 | 6837 |
| 69 and 85 | 5865 |
| 103 and 138 | 14214 |
| 162 and 72 | 648 |