Least Common Multiple (LCM) of 109 and 162
The least common multiple (LCM) of 109 and 162 is 17658.
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 109 and 162?
First, calculate the GCD of 109 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 162 = 0 remainder 109 |
| 2 | 162 ÷ 109 = 1 remainder 53 |
| 3 | 109 ÷ 53 = 2 remainder 3 |
| 4 | 53 ÷ 3 = 17 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 196 | 588 |
| 40 and 21 | 840 |
| 89 and 128 | 11392 |
| 92 and 75 | 6900 |
| 120 and 168 | 840 |