Least Common Multiple (LCM) of 138 and 154
The least common multiple (LCM) of 138 and 154 is 10626.
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 154?
First, calculate the GCD of 138 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 154 = 0 remainder 138 |
| 2 | 154 ÷ 138 = 1 remainder 16 |
| 3 | 138 ÷ 16 = 8 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 152 | 12008 |
| 200 and 200 | 200 |
| 175 and 171 | 29925 |
| 167 and 96 | 16032 |
| 118 and 109 | 12862 |