Least Common Multiple (LCM) of 109 and 168
The least common multiple (LCM) of 109 and 168 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 109 and 168?
First, calculate the GCD of 109 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 168 = 0 remainder 109 |
| 2 | 168 ÷ 109 = 1 remainder 59 |
| 3 | 109 ÷ 59 = 1 remainder 50 |
| 4 | 59 ÷ 50 = 1 remainder 9 |
| 5 | 50 ÷ 9 = 5 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 140 | 19180 |
| 69 and 14 | 966 |
| 97 and 18 | 1746 |
| 123 and 16 | 1968 |
| 30 and 168 | 840 |