Least Common Multiple (LCM) of 102 and 138
The least common multiple (LCM) of 102 and 138 is 2346.
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 102 and 138?
First, calculate the GCD of 102 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 138 = 0 remainder 102 |
| 2 | 138 ÷ 102 = 1 remainder 36 |
| 3 | 102 ÷ 36 = 2 remainder 30 |
| 4 | 36 ÷ 30 = 1 remainder 6 |
| 5 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 176 | 5456 |
| 141 and 142 | 20022 |
| 13 and 21 | 273 |
| 114 and 68 | 3876 |
| 57 and 87 | 1653 |