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 |
|---|---|
| 24 and 160 | 480 |
| 184 and 96 | 2208 |
| 164 and 85 | 13940 |
| 157 and 10 | 1570 |
| 120 and 191 | 22920 |