Least Common Multiple (LCM) of 138 and 84
The least common multiple (LCM) of 138 and 84 is 1932.
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 84?
First, calculate the GCD of 138 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 84 = 1 remainder 54 |
| 2 | 84 ÷ 54 = 1 remainder 30 |
| 3 | 54 ÷ 30 = 1 remainder 24 |
| 4 | 30 ÷ 24 = 1 remainder 6 |
| 5 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 57 | 5700 |
| 14 and 40 | 280 |
| 153 and 196 | 29988 |
| 178 and 23 | 4094 |
| 145 and 127 | 18415 |