Least Common Multiple (LCM) of 138 and 168
The least common multiple (LCM) of 138 and 168 is 3864.
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 138 and 168?
First, calculate the GCD of 138 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 168 = 0 remainder 138 |
| 2 | 168 ÷ 138 = 1 remainder 30 |
| 3 | 138 ÷ 30 = 4 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 35 | 2765 |
| 107 and 19 | 2033 |
| 183 and 176 | 32208 |
| 197 and 34 | 6698 |
| 84 and 45 | 1260 |