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 |
|---|---|
| 74 and 76 | 2812 |
| 179 and 182 | 32578 |
| 117 and 79 | 9243 |
| 126 and 27 | 378 |
| 176 and 53 | 9328 |