Least Common Multiple (LCM) of 105 and 162
The least common multiple (LCM) of 105 and 162 is 5670.
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 105 and 162?
First, calculate the GCD of 105 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 162 = 0 remainder 105 |
| 2 | 162 ÷ 105 = 1 remainder 57 |
| 3 | 105 ÷ 57 = 1 remainder 48 |
| 4 | 57 ÷ 48 = 1 remainder 9 |
| 5 | 48 ÷ 9 = 5 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 155 | 4340 |
| 173 and 185 | 32005 |
| 40 and 198 | 3960 |
| 153 and 156 | 7956 |
| 45 and 172 | 7740 |