Least Common Multiple (LCM) of 168 and 109
The least common multiple (LCM) of 168 and 109 is 18312.
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 168 and 109?
First, calculate the GCD of 168 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 109 = 1 remainder 59 |
| 2 | 109 ÷ 59 = 1 remainder 50 |
| 3 | 59 ÷ 50 = 1 remainder 9 |
| 4 | 50 ÷ 9 = 5 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 38 | 1254 |
| 42 and 39 | 546 |
| 152 and 32 | 608 |
| 112 and 96 | 672 |
| 135 and 24 | 1080 |