Least Common Multiple (LCM) of 84 and 138
The least common multiple (LCM) of 84 and 138 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 84 and 138?
First, calculate the GCD of 84 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 138 = 0 remainder 84 |
| 2 | 138 ÷ 84 = 1 remainder 54 |
| 3 | 84 ÷ 54 = 1 remainder 30 |
| 4 | 54 ÷ 30 = 1 remainder 24 |
| 5 | 30 ÷ 24 = 1 remainder 6 |
| 6 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 121 | 2057 |
| 107 and 72 | 7704 |
| 132 and 102 | 2244 |
| 147 and 124 | 18228 |
| 103 and 92 | 9476 |