Least Common Multiple (LCM) of 36 and 138
The least common multiple (LCM) of 36 and 138 is 828.
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 36 and 138?
First, calculate the GCD of 36 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 138 = 0 remainder 36 |
| 2 | 138 ÷ 36 = 3 remainder 30 |
| 3 | 36 ÷ 30 = 1 remainder 6 |
| 4 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 77 | 14245 |
| 132 and 57 | 2508 |
| 173 and 87 | 15051 |
| 32 and 126 | 2016 |
| 126 and 146 | 9198 |