Least Common Multiple (LCM) of 138 and 102
The least common multiple (LCM) of 138 and 102 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 138 and 102?
First, calculate the GCD of 138 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 102 = 1 remainder 36 |
| 2 | 102 ÷ 36 = 2 remainder 30 |
| 3 | 36 ÷ 30 = 1 remainder 6 |
| 4 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 170 | 17510 |
| 151 and 141 | 21291 |
| 114 and 98 | 5586 |
| 91 and 152 | 13832 |
| 189 and 109 | 20601 |